The bow bug I managed to somewhat figure out but not fix. Basically the followers will use the bow you give them, but not in conjunction with anything better then steel arrows. I find if I give them better arrows instead, they will revert to the hunting bow. If i give them back a good bow, they will revert to steel arrows but continue with the bow. It also helps to have no other weapons like a dagger or something and they should continually use that bow. Been using faendal for 20 levels now....hes fully equipped with upgraded and enchanted elven gear and using a dwarven bow currently. Will have to upgrade him to elven now to match.
I was using Jenassa and gave her an enchanted Dwarven bow I had improved, but nope...even with iron arrows, it was still the hunting bow.
But your second part may explain that a bit. I gave her two Daedric longswords I improved and enchanted, and those were her "primary" weapons. She'd (seeminly randomly) switch between using those and the hunting bow that you can't remove from her inventory.
I can't win

At least when she uses the swords she hacks everything to bits.
Well I now know why Mjoll is using a hunting bow instead of the daedric bow I made her! Also what's up with rings and companions? I gave her one that increased her light armor but she won't wear it she was using the ring you get from getting married but she won't even equip that again.
From my testing, they will use whatever you give them that has the most VALUE. If you give them a cheap silver ring that you enchanted with something great, but they also have a more valuable but less useful ring in their inventory, they'll equip that.
Also, if your follower doesn't wear any ring or amulet, take on thing they are wearing (like a piece of armor) out of their inventory. This seems to "reset" what they equip themselves with. You can then give whatever you took back and they should put that back on as well.
Im not sure whats up with all your guys' companions....Faendal wears all the armor I give him including rings and uses the bow I give him (so long as I don't give him any better arrows then the steels he uses). The only thing I make sure of is that he has nothing else but his armor (or armor of crappier quality) in his inventory.
That works if you only want them using archery, but I need their help in melee sometimes. Plus, it's silly when they're trapped in a corner by some baddies and still trying to fire their bow.
All I know is that this needs fixed in an update.