Yes, it is. For example, "I am thankful for the support of my friends and family."
It is incorrect. "I say" is the right one.
I would say that "support to" is used to mean a literal support such as to hold up a roof. He added a steel brace to give more support to the roof. I would say "support for" to indicate approval for...
yes.
Say either "her and me" if in the objective case or "she and I" if in the nominative case; never "her and I" which shows inconsistency in case use.