If I don't choose to prestige, can I still gain experience?

Solution 1:

No, you do not gain additional XP, and any XP you gain over the amount needed to get to "prestige rank" or level 81, is lost. You can gain weapon XP, but know that your weapon XP will completely reset every time you prestige, even if you choose to unlock that weapon via a prestige token.

If you're close to finishing a big challenge, you might hold off on prestige mode, but all you'll be doing if you wait and finish is unlocking a new title and/or emblem at best. You can generally tell if a challenge will unlock a title or emblem by looking at the appropriate challenge in the Barracks. Challenges that will unlock new titles or emblems at the next level have a small title or emblem icon with a "lock" over it. The other rewards from challenges (generally just XP) will not carry over to your new prestige.

Emblems and titles are really the only things that carry over from prestige to prestige. Most challenges will also reset, and you could do them again, but you won't unlock anything new. Notice also that there is a special set of challenges/emblems that can only be unlocked after the first time you prestige. Some of these are "lifetime" challenges that do not reset on additional prestiges.