Are my deeds and prayers accepted with masturbation, and do I have the right to custody of my daughter to raise her religiously?

Repentance for past abominations is accepted. However, sincere repentance for continuous sins like "masturbation" is obligatory, and this involves abstaining from the sin, regretting it, and resolving not to return to it. The girl born out of wedlock is not your legitimate daughter. Good deeds are accepted even while persisting in sin, but persistence in a minor sin can turn it into a major one, and it may deprive a servant of obedience. Therefore, one must hasten to offer sincere repentance.