My ex has a close friend that I'm going to try to get with.
Getting with your ex's friend could cause problems, why do you  want to get with them?
I'm just trying to get back at my ex. While I love them dearly, they broke up with me because I cheated on them.
I think that this is going to get messy. You should not try to get with your ex's friends, especially if you are just being petty and trying to get back at them for hurting you.
I do care about my ex, but I don't think it will be a big deal.
You say you love your ex, but getting with their friends isn't a good thing and it definitely is not a good way to show that you care about them. If you want to get back in the good grace's of your ex you need to not be manipulative, but rather treat them with the kindness and respect they deserve. You should also apologize for cheating.