If I could receive some guidance on these questions, I'd be ever so grateful.
1) How can a governor's message power affect legislation in a State?
2)What does the fact that aliens generally are not allowed to vote show about American beliefs?
The governor is the most important political person in a state. For that reason, s/he carries a lot of importance with the legislature, especially those within his/her same party.
I don't know of any country that allows people who are not citizens to vote in elections. Voting for leaders is a privilege for citizens.