My oldest used to suck her thumb and twirl her hair (or anyone else's who was nearby) when she was tired or needed to soothe herself. The hair twirling eventually stopped on its' own. The thumb sucking finally stopped when she fell on her front teeth and they were too sore to suck her thumb. Nothing I'd recommend but it did make it stop. As a child, I used to pluck the fuzz off my blanket and roll it around in my fingers. My very first memory is of me plucking a blanket in my crib as I was waking up and someone moving the blanket so I'd have a fresh area to pluck.
The way you describe it doesn't sound like Trichotillomania but I'm no expert. My niece had Trichotillomania and would shave her head. She moved on to plucking the hair on her forearm, eyebrows, eyelashes, etc. To me, it sounds like your daughter is absent-mindedly doing it rather than compulsively pulling out her hair.
I would try to redirect her right hand to a blanket or stuffed animal or doll's hair or something else. You will probably have to search around to find the perfect texture. I'd even take her to a fabric store and see if something there appeals. I've seen stuffed animals made of rabbit fur or from old mink coats.
As for the finger sucking, I would try to not make a big deal out of it and instead redirect her. When you see it happening, talk to her so she has to answer you. Tell her you cannot understand her when she speaks with her fingers in her mouth. When you read to her, have her hold the book so her hands are busy. Look for ways to keep her hands out of her mouth and hair without saying, "Stop sucking your fingers".
I would avoid shaving her head at all costs and instead cut the other side so it looks more balanced. Shaving her head seems like a punishment rather than a solution but that's just my opinion.