1 & 2 read the PHP manual about pconnect() and then proceed to forget about it because it's only good for large servers with hundreds of connections/sec.
You MUST use the mysql_connect() for EVERY script that needs a database connection.
3 MySQL has a limit of around 1000 unless I am much mistaken.
What happens when the limit is reached? Then the server will refuse to open more connections ofcourse.