I've been on the shot for 5 years. I got my shot July 4 and was suppose to return September 20 but in that time I got on birth control pills. I recently had sex with out a condom but he didn't ejaculate in me is there a chance of worrying about pregnancy

You should be ok. If you received a dose of Depo Provera (medroxyprogesterone) on July 4th, you should be covered contraceptively until October 3rd. So right now, you are probably safe (as safe as you usually are on Depo). But all methods do have a failure rate, so if you don't get a period at the end of this birth control pill pack, then you should take a pregnancy test.
Yes. No method is perfect and particularly when you are switching between methods. If you are worried there are excellent tests for pregnancy which are quite accurate. The most accurate measure beta chain HCG in the blood and are + 5 days after implantation of the fertilized ovum.
Probably ok. I usually recommend a condom back up when you change birth control. I would do a home pregnancy test just to be safe, but you're likely ok.