Hi!
Kamila is not very common name in Russia (but very common in Tatarstan as far as I know) but of course it is OK to use it, your name sounds very beautiful! The diminutive form may be Mila ("Mila" is similar to russian word "милая" which means "nice", "sweet", "lovely") . Mila is also a diminutive form of Russian name Lyudmila.
I don't know any other Russian names except Aleksandra (and Alexandr - for men) that have the diminutive form Sasha.