All steroids can cause hairloss to a certain extent. However, anavar is not known to be particularly bad in that regard. So it is pretty safe for the hair. If you are concerned about your hair, you should avoid highly androgenic compounds, which you should not use being a lady.
Anavar is pretty mild in the way of side effects but YES - it will cause hair loss. Any steroid will speed up hair loss.
The best thing you can do to prevent hair loss on cycle is daily use of a rogaine spray and daily use of a good anti hair-loss shampoo like n2shampoo from n2bm.com
It can but I would not worry much about that side effect. Anavar is probably the most hair line friendly and 10mg is not a high dose. If you are still really concerned then just go with SARMs.