I don't know how to see the recent sent friend requests but you can go to your own page (click your name on the top) and see your own Activity News Feed. It should list the walls you've recently written on.
You can use the 'Search' at the top, write their name in, and it will take you to a list of everyone with that name. Click on the one you want, and a box will come up and you can ask them to be friends that way. There are other ways of doing it, but I'm brand new to FB and can't really explain the other ways.
^I don't think there's a way to see a list of people that you've sent friends requests to. I've tried to do this and search and there's no way that I found. The only thing I found out is if there's a person you DO remember, search for their name. If it says "friend requested" it means you've requested them as a friend but they haven't gotten around to accepting or ignoring the request yet. If it gives you the option to request them as a friend again, then that means they hit "ignore" on your first friend request.