I deleted my old Facebook account and now have a new one. There are some people who I was friends with on my old account, but it's not giving me the option to request them with the new account. What can I do?
As far as Facebook is concerned, your new account is a completely different person. There's no relationship between your old and account and your new account, so Facebook is enforcing the privacy settings of those people. If they have their privacy settings so only "friends of friends" can make friend requests, you'll need to be friends with one of their other friends first. Quite likely they changed their privacy settings since you friended them with the first account.