How should I conduct myself for my non Jewish father (my mother was Jewish) concerning halachot of mourning for parent. The community I live in are not aware my father is not Jewish.
I am sorry to hear about your loss. Essentially since your father was not Jewish and you don’t have “yichus” to him, the halachot of mourning will not apply to you, similar to a ger whose father died, that the halachic obligation to mourn would not apply. However, it is permitted and correct for you to show respect for your father and observe a degree of mourning. The amount is up to you, whatever you feel is correct. One point is important, since halachically you don’t have to mourn, you can not be lenient as a result of the mourning, for example, on the first day of mourning you would still have to put on teffilin, you are allowed to learn torah, etc.
Suilchan Aruch 374-5, Rema Y:D 374-6.