You can be nude, you can be dressed, in just your underwear, you and/or your partner can wear some bizarre outfit, whatever you want!! As long as your bits can reach her bits, you can have sex.
Most people prefer being nude because seeing the other person's nude body turns them on, because we generally associate nudity and sex. The skin-to-skin contact feels good, and intimate, which all contributes. Because touch/massage/licking/tickling with a feather/slurping honey off parts of the body other than just the genitals is a turn-on - that applies to men, but even more so to women.
So, nudity is not necessary, but it has its benefits.
You don't have to be fully nude. Although Judy is right, it's better to explore the body that way. However, not to give too much info but last night I wore my fiance's oversized t-shirt to bed and we did the deed with the shirt on. Sometimes I leave on a bra or a sexy tank top. It's whatever feels right at the time.
Well, interesting question. Yes and no! In order for you and your parter to mutually enjoy and explore each other's body you should be nude. The human body is beutiful and there is absolutely nothing wrong with exploring yourself and your partner, but if you are uncomfortable being nudity and feel that it will take time and patience for your partner to see you fully naked, then you still can enjoy intimacy with cloth on,but with easy access availability for the right moment of intimacy.