If all assets are under $30,000 you can do a small estate. The NY courts website has a DIY program if you google New York Courts DIY Small Estate....

What type of legal representation should I seek with regards to contesting a trust and the division of family assets?

You should speak with a trusts and estates attorney who has experience in estate litigation in Surrogate's Court.

Your income is not relevant for your mother's Medicaid qualification. So no, she would not need to live alone to financially qualify for Medicaid.

I share a house with my inlaws and without consulting us they put their portion into an irrevocable trust. Plus the deed is wron

They cannot convey what they do not own, regardless of what they put on that deed. A correction deed is usually the best way to fix these things....

Can my mom sign guardianship over to me for my cousin without going to court?

Changing a legal guardian, regardless of the type, almost always requires going to court. With consent it may make it easier, but a court will need...