Newbie on the first run - Alchemist

[Berlioz]

I just started to play ToME and it's really complex, so I'm a little bit overwhelmed and have a lot of questions. I'll post them here as they come up.
I started a shaloren alchemist, because the class sounds like fun and there aren't any other mages available yet. I like zapping stuff with my wand and blowing things up with bombs. Also I think it's good to have a pet, I can learn from its mistakes. I use the alchemist guide in the mage forum as a reference to avoid the worst talents, but for a new player it leaves a lot of stuff out.
I play on normal and roguelike. I do have some experience with roguelikes, especially nethack, although it took me 5+ years to ascend the first time... I also played Dungeon Crawl: Stone Soup once, but the endgame did not appeal to me, so here I am.

What I did so far: I went into the cold tree, but I'm not sure that was wise, maybe I switch to a different infusion later. I'm going with bombs + eye beams for the first levels. After the eye beams failed a few times I figured out that the spiffy long sword my golem used disrupted them. But now it's all working fine.
So far I cleared the starting area and the Trollmire 1-3. The warrior escort in the Scintillating Caves gave my golem vitality, which works great, it died only once. In Trollmire I got an anorithil escort quest, so I learned the light tree as the guide suggested. Character level is 7.

Questions:
1. Money spending: I bought the combat tree for my first 50g, which probably wasn't a good decision, because I can't take most talents for now anyway. I do have around 70g plus around 50g in gems, so what should I buy next? There's a +health lantern in Derth, but it's kinda expensive at 67g and I alredy have a normal lantern. Shall I buy some kind of wild infusion to be able to purge negative status effects? I use Phase Door/Shielding/Regeneration.
2. How important is light radius? I'm kinda afraid of the dark, since I'm a squishy ranged class. The +2 from the lantern seem woefully inadequat. Shall I buy things with +light radius?
3. Shall I imbue stuff with gems or is it a waste of money? If yes, what are the most useful ones?
4. I got a Crystal Focus from the starter area boss. What shall I use it on? Right now it's on my starting staff, but it's kinda underwhelming.
5. I gave my golem a shield, is that good, or is a 2h weapon better?
6. What are the two "gem" slots on my golem for? I cannot put anything in it.
7. My armor lets me use "track", is that useful?

[Razakai]

1. Combat Training is very important to get 1/5 in the Armor Training skill so you can use gauntlets/helms. Save +str gear and use that to meet the requirements, can unequip after taking it. Obtaining a lantern with a good light radius early on is important, look for +4 or more. +hp on items is also good. And you absolutely need a wild infusion for physical debuffs as stun will kill you. One for mental to deal with silence can also be useful.
2. As above - you want a good light radius or infravision.
3. +all damage/crit, resist all/armor are probably the most useful ones. Definitely worthwhile. You can find artifact gems later which should be saved for a good bit of gear as they're powerful.
4. Crystal Focus is less useful for a caster, but still decent. Keep it around until you find a better staff. Later you can find a Crystal Heart which does the same but for body armor, combining the two gives a powerful set bonus which might work with your channel staff attacks.
5. 2h is probably better as the golem doesn't have any shield talents. Generally best to just give it the strongest weapon you can find.
6. The gem slots are unlocked via the Gem Golem talent.
7. Track is very useful albeit tedious. Using it regularly to scout out dangerous enemies can save you, but it's a very slow and boring playstyle so only use it in areas you're scared of (useful in Lake of Nur as you can avoid the powerful horrors for example).

[Dopaminka]

50g is nothing and the category is great to have/must-have for the armour talents and Thick Skin.
You are the only class with Stone Alchemy unlocked from the start so put it to good use you'll have a crapton of gems late game anyway.
You can often buy a good lantern in Derth shop. Halflings greatest invention ever was their Bright Brass Lantern of Health.
Gem slots on golem are for advanced golem skill category.
Track is useful on higher difficulties, not so much on normal probably.

[Arcvasti]

Alchemist is a kind of fiddly class, but you can easily make them work on normal. You probably want to get stuff from all of the elemental trees, honestly. Caustic Mire and Dissolving Acid are especially nice for slow and sustain removal. Flash Freeze and Ice Core are also really good defenses against melee rares, which can deal large amounts of damage.

Infusion choice doesn't matter that much, but there's still some strategy involved. Fire is best for damage since Smoke Bomb is stupid and +fire items are easy to find. Acid isn't resisted by many enemies and your second best damage spells are acid-elemental. Lightning Infusion just isn't worth it, although Thunderclap and Living Lightning are good enough that Energy Alchemy is still worth unlocking. I've never really used Cold since constantly freezing enemies is annoying, but a frozen enemy is an enemy that isn't attacking or healing, so it's probably still pretty good.

Note that I have not mentioned the golem. The golem is good for bodyblocking, carrying items and eye beams in the T1s and that's basically it. You'll still want to keep it's gear and runes up to date, but don't prioritize the two golem categories or anything. They're still worth investing in eventually, but you want your debuff spells online first.

For equipment, I'd recommend going massive armour. Armour is a much better stat then you think it is and Alchemist really doesn't have mana problems. Track is nice, but you can get it from thief escorts or gloves, so I'd prioritize +hp or armour on body armour.

Windborne Azurite, Lifebinding Emerald, Goedelath Rock and Petrified Wood are all good artifact gems, ordered roughly in order of how good they are. You definitely want one of those on your endgame body armour. Before that time, putting in a stun resist gem like quartz or bloodstone is pretty helpful.

[Berlioz]

Thank you all for the great advice!
I've bought a +5 lantern in Derth and some +health items. The laser shooting golem then finished the T1 dungeons all by himself.
Since I found primarily fire stuff I switched to fire infusion. I have only 1 point in cold and I wanted the smoke bomb anyway. Money is good, I actually cannot find stuff I'd like to buy.

[Berlioz]

Soooo, I finished the easy stuff, but without finding good stuff, except a blood vial. Oh and my golem beat up Bill with his own Tree Trunk.
The mage guy near Dearth wanted an "arcane artifact", took me a while to figure out he wanted a [unique] item. Maybe should say [artifact] or something. I had none, but I found some tunnels with rogues and thieves in it. I nearly died several times by being surrounded out of the blue. Only teleports and gem portals let me survive. The rescued merchant doesn't have good stuff either. I'm now lvl 14 and Dearth has been invaded. I went into the Forest, but barely escaped with my life. I feel that I need better gear or more levels to be able to beat anything. I went and hunted patrols and adventurer parties, but got very little gear. The golem got a new weapon, but it cannot use the T3/T4s that drop and I cannot get gems from them either, because I lack the talent. Got a unique dagger for the mage though and bought some new jewelry in the mage city.
At this point I fear I need more help.

Questions:
1. I drank the Blood Vial, I now have a second life, right? Is the vial good for anything else?
2. When do merchants restock their wares?
3. I get less and less money for stuff, is this normal? Does it also affect gems? I have around 300 by now, mostly T2.
4. Is there something I can use all the money for? Because I already bought the few useful things in all the shops.
5. Can I access more towns? I got the halfling one, the elven one, Dearth, Last Hope and newly found mage one.
6. After clearing all the T1 dungeons, arena, lumberjack village and tunnels, can I get more XP/gear before going into the T2 dungeons? The patrols give barely any of those.
7. I found a shield rune I gave my golem and bought a lightning one as well. So it has 2 shield + 1 lightning. Is that good or shall I look for something else?
8. The alchemist guide said something about a "Sher'tul fortress shade", where do I find that?
9. At what level can I try to rescue Dearth? Do I need special gear?
10. There's this hermit called Agrimley who wants me to find alchemist stuff for his potions. Which one should I choose?

Okay, wow, that got a little out of hand. On the plus side I unlocked Cursed and Summoner, although I have no idea how I did the latter. It was in the middle of a fight with several rogues in the tunnels.

[Arcvasti]

1: Nope, that's all it's good for.
2: After Dreadfell, which is a ways away.
3: No and I really suspect you're not actually getting less money as you go along. It almost always gives more money to transmute to gems and then transmogrify the gems.
4: Eventually, yes. The merchant you saved from the tunnels gives you randarts for 4k gold apiece late-game.
5: Not until after Dreadfell. There are two elven ones though, one in the forest near derth and one past the south forest. Make sure you do the dungeons near both towns before starting on T2s.
6: Not unless you missed shatur or elvala dungeons when you did the T1s earlier. You shouldn't have any problems in T2s as long as you use throw bomb on cd and are always ready to escape with gem portal.
7: I like giving the golem acid wave rune for disarm or rune of the rift for banish. Lightning is decent though.
8: Under the Lake of Nur, at the end of the Old Forest. I wouldn't go there until you're done with T2s,
9: Once you're done T2s. The boss is brutal the first time you fight him, but there's a trick. Just activate your movement infusion before fighting him so he can't hurricane you. His health is pretty low, so you can kill him quite quickly. If you don't have a movement infusion, then get one ASAP. Your inscription loadout should be something like heal/regen, phys wild, movement and heroism[Or shield if you haven't found a heroism yet].
10: Focus gives +2 class points, which is leaps and bounds better then the others. There's an alchemist in last hope who has a potion that gives +2 generic points, which is even better.