Can you :

1)Teach Serana new spells ? (buy her the spell book and she will read it )

2) Get her better armor(I've given her other armor and weapons and she will equip a weapon I gave her, but not armor).

Thanks

PS I'm playing SKYRIM with SKYRE mod and some visual enhancements.

1) no she only uses her default spells
2) if the weapons and armor you give her are better than her default armor and weapons then yes she will use them. I think she only uses light armor so if you give her heavy she won't use it.

1- Not on console, but since you're on PC, its very likely there's a mod fkr it.

2- I've always been able to give her different armor.

In order for a follower to wear new armour, the armour needs to have a better AR than the followers current attire.

I gave her and she wears them.

you are on PC you can use follower overhaul mods there are several on nexus they will allow you to set armor type for each of your followers you can give them various sets like armored for travelling and combat and clothing for cities and towns and follower will do exactly that you can change their combat styles like make lydia master wizard, make jzargo master archer kinda thing, teach them new spells but these mods only support game spells not modded

I stand corrected then. I guess she can wear heavy armor.

I just thought I would say if you give her an armor with a better rating than her default and she still doesn't put it on, try going into another screen and she might be wearing her new armor. I noticed this when I tried giving her armor and was wondering why she wasn't equipping it.

I noticed in a previous game i was married to Jordis. I think she wears steel armor by default. One time i gave her a full set of ebony armor. Outside of combat she kept her default equipment. Once i asked her to follow me all of a sudden she donned her ebony.

Thank you all

I appreciate the prompt and strong response.

I'll just have to make sure she gets better armor than I've offred so far.

1) No. In order to learn new spells you have to read spellbooks, and sadly you can't force her to do that.

2) Yes you can, but not right away. In the very beginning she refuses to trade stuff with you.