Is the man considered a murderer of his infant daughter who was born with deficiencies and died after two weeks, given that he regularly beat his pregnant wife and wished for the fetus's death due to problems between them?

If it is medically proven that the death of the child was a result of your repeated beating of your wife, then you are liable for ḍamān (compensation) and kaffārah (expiation). Aside from that, you must repent to Allah for your injustice towards your wife and your ill-treatment of her. Beating is only permissible for disciplinary purposes after admonition and boycotting, and it must be a non-bruising beating that does not break a bone or disfigure a limb. Striking the face is not permissible.