I don't believe that leveling the bow skill line itself increases bow ability damage, but increasing the rank of individual abilities does. Bow abilities scale off of weapon damage and stamina, so will need to decide where you want to put your resources.

Someone else might be able to give a better explanation of exact stats and numbers, but I can give you a general idea.

Damage is determined by a weapon's damage stat - higher level weapons do more damage than lower level. It's also affected by any secondary enchantments you have on the weapon. There are some passive skills you can unlock to increase damage and criticals, but just plain leveling a Bow or any weapon will not increase damage output that I'm aware of.

For leveling the bow (and really any weapon), points in Magicka/Stamina don't matter. Magicka and Stamina simply determine how many times you can attack with a particular skill on your hotbar - when you run out of magicka/stamina, you'll only be able to do regular mouse click attacks.

You level a weapon by doing several things:

-Just having it equipped and exploring, unlocking treasure chests, and discovering locations.
-Killing enemies with it.
-Turning in quests while having it equipped.
-Using the various weapons skills attributed to it in combat, though this kinda falls under the category of killing things.
-Finding a Skill book on the various bookshelves throughout the world and reading it. (These give a full level, and will offer a weapons skills, class skills, and crafting skills depending on the book. However, they will only offer it once. Reading the book again, even on another bookshelf, will not give you another level.)

Oddly enough, you can also level a weapon simply by having a skill from it on your skill bar. For example, I could use a skill point to unlock one Bow skill, put it on my hotbar, and promptly switch to using a healing staff instead. Even though I wouldn't be able to use that Bow skill in battle while I was using a healing staff, Bow would still gain levels.

Now, to level up the individual skills that a weapon has, you must:

-Have it unlocked by spending a Skill Point.
-Have it slotted to your hotbar.

Once you've done these two things, the above weapon leveling stuff applies, though obviously they'll level faster through constant use in combat. The faster you level them, the sooner you can morph them to gain an extra effect or ability for the skill, something that's typically pretty worthwhile to do.

For archery, Stamina is definitely a good thing to get, but there shouldn't be any real problem spending attribute points on Magicka and Health unless you really under-develop Stamina. I don't have exact numbers on it, so I'd recommend searching the forums/Google, but there are soft caps built into attributes - if you increase them VERY unevenly, you'll start gaining much less of an increase to stats than you normally would.

Hope this helps!