So did they fix the glitch where followers would only use hunting bows even if you gave them a better bow?

I believe they did - I've given Zephyr to Lydia, and she uses it. They won't have infinite arrows for any bow other than their default, though. You'll have to keep them stocked up.

ETA - actually, the infinite arrow bug was fixed by the USKP, So never mind that.

So what about characters which don't originally have a bow in their inventory but use a hunting bow for long range? I had Rayya with me when I was making her Ebony Armor and she pulled a hunting bow even though she didn't have one in her inventory.

Any follower who is tagged with the Archery skill will have a hunting bow and iron arrows as part of the default inventory. All follower default inventories are "hidden" - the items don't show up in their Trade dialog.