Should I keep visiting my male cousin as often as I visit my sister or aunt or daughter especially if that cousin is away from Islam? Is it okay to stay away from him to avoid Fitna? I've told him to change his ways but he does not?My aunt (wife of my father's brother) is 55 yrs old, she has lots of sons; one of them is my age. When she visits my family, she usually shakes my hand and kisses on my cheeks. She does the same with my father too. She does this in front of her husband and children. Is it Haram or Halal to do such a thing?In case, friends, neighbours or family ask for money or car, etc. whom I know don't have Islamic principles is it okay for me to try to avoid them. So I don't have to be in an awkward situation of their asking and my refusing?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

As for your cousin, scholars of Islam differ whether he is from among the blood relations whom we have to join and co-operate with them or not. Anyway, your cousin is one from among the relatives and you are required to treat kindly and politely.
As to your aunt, she is not from the Mahaarem (unmarriageable persons) to you or your father. So, it is Haram to shake your hands or to kiss your cheeks even if she is a hundred years old. It is your duty to hear such a ruling and to avoid such prohibited action.
Allah, The Great and Almighty, has ordered us to treat neighbours kindly. He Says (interpretation of meaning): {…and do good to parents, kinsfolk, orphans, Al-Masâkin (the poor), the neighbour who is near of kin, the neighbour who is a stranger, …} [4:36].
Know that a near Muslim neighbour has three rights: right of relation, right of Islam and right of neighbourliness. If he is not near you, then there will be only two rights. But, a non-Muslim neighbour has only the right of neighbourliness.
A neighbour is not obliged to give his neighbour money or car unless there is a dire need that if not satisfied a serious danger may exist.
To give advice to your neighbours is a form of kindness, especially if your neighbour is negligent or sinful. On the contrary, to boycott your neighbour is a form of one's bad act against one's neighbour unless your neighbour shows his dissoluteness and you consider such a boycott more probable to deter him from his dissoluteness.
Allah knows best.