To be a little more detailed:
screeg wrote:Do archers suffer any penalty for attacking adjacent enemies with the bow?
If you mean attacking by using Shoot and other talents, then no. However, enemies that get adjacent to you often have nasty melee attacks, so it's generally a bad idea to fight in melee. If you mean just bump attacking with the bow in your hand, then you don't suffer a penalty per se, because the bow is already a terrible melee weapon.
Either way, try to avoid melee combat. I mean, don't waste stamina Disengaging from a giant rat or something that you can reliably one-shot, but as a general rule, you are a ranged combatant and should exploit that to the fullest.
Do you have to keep your default arrows replenished? Can you run out of basic arrows?
As lukep said, you get unlimited Reloads, no matter how magical your arrows are.
Does it make sense to invest in melee weapons at all, or should I pump ranged weapons exclusively?
You'll be worse off at melee combat than any dedicated melee fighter. The only melee talent trees you get are Dirty Fighting and Combat Techniques (specifically, Rush; the other talents should work just as well at range). Both are locked and should remain locked; you have much better things to spend your precious category points on. The only other way to really "invest" in melee combat is to take the Weapon/Dagger Mastery talents. You should not take the Weapon/Dagger Mastery talents. All the "proper" melee fighters take Weapon/Dagger Mastery
and a plethora of other melee-boosting talents; you'll never come close to their skill in melee.
Now, if you really want to play a ranged/melee hybrid, you can take a melee character to a Last Hope weapons store to teach them how to use bows and slings. They don't get any of the Archer's talents, but some melee classes can unlock those trees. Such builds are usually suboptimal, though. I hear Rogues can get some mileage out of using slings, but I'm terrible at Rogues and all variations thereof, so I can't speak from experience.
My advice? Once you're feeling good and confident, poke around Daikara for a bit. There's a sidequest there that unlocks a class all about combining archery, melee, and spellcasting.