There was a bow in one of the cells in the starting cell block (far left, centre), though if you have already jumped down the pit you will not be able to get back there for awhile (you will get access to the battlefield before then, and can check with the merchants there).
Unfortunately, there is no way to automatically switch attack types or weapons. While some games offer more AI control than BD, I don't think I've played a game yet with a mage in a party where I didn't have to control the mage myself to get acceptable mana use and (where applicable) spell selection.
Someone who has played a mage may add their comments, but I would suspect the best control method would be to have the standard attack on the LMB and during fights switch control to the mage to cast spells with the RMB. If you want to auto-attack with magic, you can assign hotkeys to switch attacks on the LMB, but I think you would still need to switch to the mage as the leader to use it (so if you wish to control the warrior, it would take 3 key presses to switch leaders, change attacks, and switch leaders back).
Once you get a bow you may want to just let your mage auto-attack with that for weaker opponents, and then manually switch to magic during tougher fights. For the majority of the first act there are lots of skeletons around, which are more vulnerable to crushing damage than piercing, so the lack of a bow isn't a big disadvantage. Until I reached the citadel I had my hero use crushing weapons (a club or 2 handed walking stick) most of the time and a bow for tougher fights, then I switched to archery full time. My DK continued to use slashing damage (1 or 2 handed swords).
