3. Can you acquire a golem during play or only at creation.
Take the golemancy tree. That the only one giving a golem.
4. Alchemists, archmages, and necromancers regenerate mana naturally. Is it possible for adventurers to regenerate mana naturally? (I assume "no").
Any point spend in any spell requiring mana, give mana regen at 0.25 for adventurer
5. Brawlers get improved attack speed with gloves.
You only get the 166% speed with any point spend in one of brawler trees: Unarmed mastery, or pugilism, or grappling, or finishing move, or unarmed discipline (not Mobility). That 's the only way to get the special speed, and skill/spell proc from gloves.
6. Cursed and Doomed characters can learn the "cursed aura" tree the first time they pick up a weapon.
 as stated by 64Lego you get Cursed Aura with 1 point in Unatural body.
7. Some classes start with free points in armor training, especially shield-using classes (so they can use shields). Is there any way for an Adventurer to get free armor training (I assume "no").
Those point are free? Are always assumed they were taken from your pool. Eg: Bulwark as less generic point to spend than other.
Adventurer don't get free point. The Combat training tree can be bough for 50 gold in Hope.
8.Can you still use spells and arcane items?
As of 1.3 you cannot use spell or arcane item if you have a point spent in Antimagic. You could in previous version.
A few other Adventurers shenanigan:
To get the Soul resource (necrotic aura) you need to get the Necrotic minions tree. That the only one that gives it.
Mindstar and Staff Mastery are sold in Zigur and Angolwen respectively.
The tree from Solipsism class don't give you all the feedback resource (solipsism, dream forge, ... does not) . I assume only the one using feedback (Discharge ?) or just Feedback.
You only get Spacetime tuning when you spend a point in a chronomancy spell with a paradox cost (activated, or sustain). A point spent in passive chronomancy skill will not give you the ability, and you'll be stuck to a 0 default paradox level. Chronomancy passive is my actual go to, as an adventurer. With 1000 paradox you can get some nice passive bonus (fold!!)
1 point in corrupted strenght give one free melee attack after a spell whatever the weapon in hand: 2 handed, 1 weapon and a shield, dualwielding, or even unarmed.