1) Do you have to subscribe monthly to play FFXI? Or are you charged per character? Either way- how much is it?
$12.95 a month, and an additional $1.00 for another character.

2) I use my PC for online gaming- can I use a dial-up connection to play this game or do I need broadband? If I can use dial-up will the game suffer from massive lag or is it still playable?
You should be able to play, though you may run risk of being disconnected far more often.

3) I know many patches exist for FFXI- if I buy the latest version will I still have to download them all or will the game already be updated via an expansion pack?
I don't believe so. You'll probably have to do all the patch downloads. That took me four hours with DSL when I switched it over to my new computer. With 56K, you're in for a ride.