i think i read this rule somehwere.. that you are eligible to apply even if you are a student of a temporary worker in canada... i'll try to fine that article and give you the link
anyone can give the invitation for visit visa.. not necessarily children.. and if your cousin is giving the invitation then they dont need to mention your name at all.. your parents would be goign to canada to visit your cousin
letter should be directed to his brother.. because his brother would gather all documents and make an application for visit visa.. no idea about the other question
all depends on how satisfied are you with the country you are living in right now.. a country or a city never makes us a part of family.. we have to establish ourselves and make it OUR city.. you can enjoy even in the worst city in the worl and still cry in the best one