Resolved questions
How does it use the "UP"

In English we have these things called "compound verbs". In some ways they are like reflexive verbs in that some reflexive verbs can change the meaning. Like sentir and sentirse mean to feel but in a different sense, but compound verbs can be worse. Give is "dar", but give up is to surrender "rendirse". My Spanish professor taught us that these do not exist in Spanish, and often cause Spanish speakers a lot of confusion. The example he used is that buildings burn down, but when someone has a fever they say he's burning up. Buildings burn down, people burn up.

You just have to sort of memorize every single valid combination. It's the same with other adverb-prepositions.

Some combinations are idiomatic (they have a special meaning you have to memorize), like:

stand up (for someone or something)
stand in (for someone)
stand beside (someone) [figuratively]
stand between (a person and a goal or objective)
etc.

Some are directional, or have two different meanings:
stand in (something, like mud) [so this one has two different meanings, see above]
stand above (something)
stand above (a group of people, meaning to be special in some way)

I even googled "to stand under" and got some results where I didn't recognize the usage, so you learn things all the time!

As Randy says, these prepositional phrases are called "phrasal verbs". Check 'em out; there are several resources at my local library that are all about phrasal verbs, so there should be some at your local library too.

Makes like a reflexive verb levantate

I agree with Randy: if you're looking for a precise definition of "up", then you will really struggle with phrasal verbs. It's best to understand the preposition ("up", for example) as a concept.

For example, "to look up" can mean either a literal look in an upward direction; a figurative look, meaning to admire (he looked up to his older brother); to find a reference or information (look up words in a dictionary); a change to a positive feeling (things are looking up).

You'll get the meaning from the rest of the sentence, but if you tried to force a single definition into all these situations, it would never make sense. Just relax and imagine the possible meaning from what you already know.

By the way, phrasal verbs are not automatically reflexive. ;)