I've only got the Depo-Provera shot twice I missed my third shot and have had unprotected sex since is it possible that I can get pregnant.

Of course yes . Anyone having intercourse without birth control or condoms may get pregnant. If intercourse was within 72 hours you consider taking plan b. Ella (ulipristal acetate) is another brand that can be used up to 5 days after unprotected intercourse. Plan b is a high dose of birth control to disrupt the hormonal patterns to delay or prevent ovulation. Abnormal bleeding after is common. Check preg test in 10 days.
Yes. The depo shot is only effective for about 3 months so if you have missed your shot you could become pregnant even if you have not had a period since. Most doctors will have you do a pregnancy test if you are late for your shot.