The UESPWiki – Your source for The Elder Scrolls since 1995
Arrows can be shot through doors (and walls if in the void).
Switching from melee weapon to bow
takes forever, unfortunately. I assume the speed attribute will help this. ..but I still think it should be faster. I usually only use my bow when the enemy is isolated from me. I attack and then retreat to wait for my bow to reload , which prevents the creature from attacking me with a ranged attack if it has one.
It's often possible to position yourself behind an object such that you can hit your opponent without your opponent hitting you (both using melee weapons). For instance, if you hide behind a shelf in a store, the guards can't hit you but you can hit them.