I just recently (four days ago) had extensions sewn into my hair and I LOVE them!
Didn't hurt one bit
But I was told to use a "mild" shampoo while washing them.
Does this mean I have to use Baby shampoo?
Also, can I put conditioner in them?
Tease them?
Blow-dry them?
What brands of shampoo/conditioner do you suggest?

It doesn't mean baby shampoo just use a clear shampoo not creamy

and only condition your ends.

you can blow dry them but try not to tease your fake hair

instead if you want some volume use a big roller where ever you need some volume

mild shampoo means no harsh chemicals or heavy shampoos that leave residues.
You'll want to use something simple, that's meant just to clean hair in basic washing, no bells and whistles shampoo.
You can tease and blow, just be gentle so you don't rip the seams out.

of coures you can do what ever you want to do with them just make sure there heat protected and when she means mild she means everyday shampoo not the professional kind you use once a week