i'm not sure if there is an easy way to increase the quality of a video although it might look better if you play it on a lower resolution though

You can't add information to a video that isn't there from the start. So, you can't add resolution or color depth. An average quality video won't get better than average. You can run some video filters to remove noise or increase gamma, but there is always a trade-off of some kind. For example, you could run a smoothing filter to reduce the appearance of blocks, but that reduces the sharpness giving a soft focus. No amount of money or technology can produce something from nothing. It's best to start with the highest quality video source whenever possible.

ugh.... I would just create a program that would predict the information based on statistics and very long hypothesises.
Of course, then i would just have to be the next John Nash, lmao

Well actually is the same as the video thing, you can "enlarge a picture" photoshop in example multiplies the pixels you are expanding at a certain amount, but then it will only enlarge it, not improve its quality; if i do that to an image that is 'medium' size all i'll get is a medium image enlarged to fit X size but things that are already out of focus, or a spot that is not well-defined in the original pic wont improve as I enlarge it. There are filters and other things that can fix a bit the image, but if for example something is too far behind or out of focus it actually takes a lot of time to fix or define in order to get something -if anything- out of it. So pretty much as with the video thing, i'd recommend starting up with an already good-quality image