I've done similar migrations and I think you're on the right track.
"How should I go about doing (1)?"
Just take a mysqldump of your DB and store it in a file, e.g.:
mysqldump -h [host] -u [user] -p[password] [dbname] > dumpfilename.sql
"Is (2) even possible ?"
Absolutely. You can connect to a MySQL RDS instance just like you would connect to any other MySQL instance. The host name is refered to as "endpoint" in the AWS Management Console.
One you've created the RDS instance and setup the security group, you're ready to load the dump:
mysql -h [endpoint] -u [user] -p[password] [dbname] < dumpfilename.sql