Yes, they do. The Canadian permanent resident card is the only proof of identification that proves, both inside and outside of Canada, you are a permanent resident of Canada.
Legally NO. You must be a CITIZEN of the United States to Vote.
This doesn't mean that it does not happen.
I believe the question and the answer given are somewhat miss-leading. The question was...
Depends where you are and previous citizenship. Western europe, a person born in the country will (usually) only face deportation on termination of prison sentence for Treason.