I’m a junior, and while I’m worrying about the AP test, I noticed that there’s ten spaces on Common App for putting down AP tests, and I am planning to take 13-14 overall. Looking at the top schools like HYPS, MIT, I know for sure that one of the AP tests that I will be taking in 2 weeks I will be getting a 3, but for the rest, I am sure that I have/will get a 5. I realize that we self-report these AP Scores, but do we also send in the official scores too? I’m worried about the eventual cost for these, and also if I could 
bury my test that I will get a 3 on.
I’m not sure that colleges need official AP reports during the admissions phase. Check clearly what their requirements are – obviously before you enroll at your chosen college a few years from now, you’ll want to send in official scores for the ones where you’ll obtain credit or advanced standing. I’m not sure that colleges need an official report simply during the admissions round.
Please let us know how you developed those prognostication skills; I, personally, would like to buy some lottery tickets.
They do not. Send in your scores when you’ve decided upon which college to attend. Send beforehand is a waste of money.
For the Common App, you can list the tests you have taken and the results, and if you still have room, list those tests you intend to take in the future. If the total is more than 10, you can use the add’l info area. However, note that AP scores carry little to no weight in the admissions process for the vast majority of colleges, so don’t spend too much time overthinking this.