That's quite a list. I'll give my immediate reactions, but could very well change my mind as I think about them more as we get into the development cycle again.
It would be more work but maybe a non-OBSE and an OBSE Vilja version would be a way to go. Or if it is possible to just have an OBSE-addon but I do not know if that is possible. As for suggestions for next version:
There will
NEVER be an OBSE specific version of Vilja, any OBSE features will be built into the mod as options/bonuses for those with OBSE or they won't happen. I don't want to even think about how horrible it would be to have two different versions with all of the dialog that Emma creates!
1. Have her automatically repair her armor if going to sleep.
2. Have her repair her armor when asked through dialog.
Those are planned. And I've got a few other triggers too. If the player is repairing armor, Vilja will repair her's at the same time. When she sleeps, if you leave her in another cell, etc. But you're going to have to keep her stocked with hammers and if you set the option for her to repair armor she's not going to give you hammers any more.
3. Use appropriate weapon if facing creatures only affected by silver or magic. If she does not have such she should stay back and hide or just heal the player if that option is chosen.
Forcing her to use a particular weapon is something I don't want to do. I hate overriding the game's AI because it only causes problems in the long run. But forcing her into a passive mode when she knows her weapon doesn't work might be OK. On the other hand why don't you just give her a better weapon?
4. Have her skills improved if using enchanted clothing or armor/weapons.
That already happens! Except that NPCs can't benefit from certain items. I have no interest in trying to implement the ones that don't in a script. Sorry.
5. Be able to use better alchemy equipment.
No OBSE required or even helpful for that. Ordinary scripting/dialog can do it.
6. Have an option on first dialog page to give her strawberries, sweetcakes, sweetrolls so I do not have to go through multiple menu options to get that.
I doubt Emma will do it. What are you doing to her that you constantly need to feed her?
7. If possible, some way to better interact with NPCs added by other mods. I only have once case right now where I had a problem. I have Frans and The Alyeid Steps installed, no other overhaul. I have the Frans Adventurers plugin which adds adventurers to the game which you can meet in dungeons. Vilja and I went into the cabe to activate the stepstone network and met two adventurers from Frans. I ws not looking at Vilja at the time but soon heard combat and she was fighting with them. We did have our weapons drawn when we ran into them. I interceded into the combat by talking to Vilja and was able to get her to stop. A few seconds later the adventurers attacked her again. Interjected again and moved away. One adventurer again came after her. Had to kill him with the console so we could continue. Further in the dungeon in an interior we ran into another adventurer and he got along fine with Vilja even when we had to fight a Minotaur Lord. I do not know how to find why the combat happened, and as the adventurers attacked Vilja after we got out of combat with them, I suspect Frans but do not know why Vilja was attacked. I am redoing my game again tonight to get a different configuration, also using Frans, so will keep an eye to see if it happens again.
That's likely just a fluke and I honestly don't see how OBSE would help. There's no general way to tell which NPCs should and shouldn't attack her.
8. Have Vilja recharge her weapons if she has full soulgems, if the weapon has 0 charge or if a soulgem would recharge it without wasting charge, unles it is at 0 then she would use the lowest charged soulgem she has to bring it to full charge regardless of waste.
To do that I would have to experiment to see how soulgems actually work but I'll think about it. (I've never actually used a soul-gem in Oblivion. I'm usually a mage, so why would I need some silly item that has to be recharged?)
9. Ability to recognize ingredients from COBL.
Maybe? That would also require me to use COBL to find out what ingredients she might reasonably find interesting.
10. Ability to make complex potions is she has ingredients in inventory (like poisons, restore attributes), potions I would ask her for. This way I would not need alchemy in my skills and just have her the alchemist in our party.
She's not supposed to be a very good alchemist! But maybe we could give her a little more diversity. One if the problems is that it's dialog based and adding more features means many more dialog entries. OBSE really don't help much with that I don't think.
11. Have Vilja recognize enchanted clothing as armor (my cheat to keep from having to repair her armor) so when told to relax she would switch those clothes to her dress. This would include hoods and cloaks which IIRC she keeps equipped even if relaxing.
That seems like it would be extremely hard, but I'll look into it. I'm more likely to just give her multiple wardrobe options and let you use one of them as the "armor" choice.
12. Enter combat if player is in combat even against NPCs she does not recognize as hostile, as in the Unfriendly Competition quest fight in the tomb.
OBSE isn't needed for that, we just need to find out which NPCs in which quests have that bug. So far we've decided there are few enough that it's not worth fixing. I just thought of one more way we could potentially fix that bug though.
13. Not get mad at all if I hit her by mistake

Not possible and I don't think it's reasonable anyway. The game already has a system to keep her from responding to being hit, but if you hit her over and over she'll eventually get mad. I think that's the correct behavior. Stop hitting her.
14. Be a better archer (although the free arrows laying around are a nice bonus).
I don't know enough about combat to even think about trying this one. Sorry.
15. Stop combat even if in combat. Example when she detects enemies through a wall. I am not 100% sure, this is just a thought now. I can get her to talk to me in this situation and she asks if I want some help. If I say nevermind sometimes she stops sometimes not, or she will resume the fight soon after. Also, when traveling, she will attack a mudcrab which may have targeted me even though I am running past them. These insignificant creatures I ignoe at times at high levels. Not worth having to repair my weapon after a slice or two. This would go hand in hand if I want to run away from combat she should run away too.
Just tell her not to attack. You've got multiple situations all described in one case here and there would have to be different solutions to each. These situations are why she has multiple attack options. Try to have a script force her into not attacking wouldn't always be the right thing, so if we did this someone would complain that she won't attack when she should. Sorry.
16. When sneaking and we come upon two enemies it would be REALLY COOL to have her target one with her bow while I target another and shoot at the same time. or even target one so both our shots can kill the target. How cool would that be?
If we would do that, it wouldn't require OBSE. It might be cool, but it would also be annoying to implement. I'll think about it.
17. Put items in her inventory that instead of shopping she can go and sell for you.
Yes, we've already thought about a "sell these when you get a chance" container.
And Arkngt, the idea for hotkeys for stay and follow sounds reasonable to me.