For example if i pay rent, does my parents home become part of my assets.
No, not any more than an apartment complex would become part of your assets if you lived in one.

Will my parents income contribute to mine, if i am self sufficient except for owning a home.
No. They are not supporting you.

Get yourself a good bankruptcy attorney to help you sort things out. BK is scary enough as it is without trying to do it without proper help.