Ik Im currently playing a thief, but I just found out you can enchant your own staffs with Dragonborn, and it makes me curious for a battlemage. Are they really worth using? Considering by the time you're doing dragonborn, you should have a very comfortable magicka pool and the arch mages robes

As you said, by the one would normally do Dragonborn, they would a large pool of Magicka. A staff is pretty much rendered useless. You would use them if your Magicka is depleted.

Ok. Also, is staff enchanting affected by enchanting perks?

You don't enchant the staff yourself, you give resources to an npc that does it for you.

I give all my staves to followers. They love using them on all and sundry.

I don't think so. They are pretty much the same staves you see on the homeland.

No, they're not. But they're affected by your character's perks in the school the staff's spell belongs to. They're also affected by relevant enchantments and potions.