The bad news is that there's no simple rule which applies to all examples of [verb] + up/out. You simply need to learn each phrasal verb as you go. I agree with Francis' advice: treat them as distinct words. The good news is that you'll eventually get a feel for how phrasal verbs work, and then you can begin to use them intuitively. This will come from understanding "up" and "out" (for example) as concepts instead of words with fixed definitions.

It absolutely makes a differece, because only some words use up or out, and they are not interchangeable. There is no rule , you just have to memorize them.

There are many English verbs that are in the form of a verb+preposition. You can treat them as distinct words. For example, take off, take on, take up, take down, take out all have distinct meanings.

In this link you can check it out 36 verbs called "frasales" https://www.youtube.com/watch?v=6J_ZE7oy8q0

You can leave out the "up" in the example above and I think it more common to just say "fold" when talking about clothes. It seems redundant but many people say "fold up the paper, etc.". If something is more complicated, like a paper airplane you could also use "fold in." I think in baking they also say "fold in." You "fold out" a convertible couch/bed and probably other things that don't come to mind at the moment. "Figure it out" is an expression you wouldn't change, though "figure" can be used by itself in many contexts.