New to all this and have questions.

Blocks indicate damaged LED elements behind the projector's LCD or a lack of calibration to even out the luminance plus of course the resolution could simply be realtively low so luminance variations within the pixel triplets/ quadruplets also show up. Otherwise you should not have much of a problem. Projections long existed before fancy control software. All you have to do is create a test pattern (grid, points) with known spacing and project it onto your target, then take measurements and photos to figure out where goes what physically and how it is distorted so you can compensate.

Mylenium

I've never set up a projection mapping, but I can tell you that no matter what, you wouldn't want to output directly from After Effects to your projector as AE is not a real-time environment. You would want to make a video or videos that match the requirements of your projector's software, so you'll have to read the manual or find tutorials from the developer of that.

As for the little squares, it's hard to tell what you mean without seeing it, but it's possible the projector just doesn't have a very high resolution and you're trying to project on a huge surface so you're seeing individual pixels.