Both "compromise" and "commitment" are given as translations in various sentences in this unit.
It's interesting that the same word is used for both in Spanish. It is also used for "compromising situation", which is yet another meaning. I'm guessing that the meaning is usually from the context in real life where you wouldn't have just a single sentence.
About "Thanks for your compromise", I think I'd say "Thanks for compromising."
I can see a clear relation between a compromise and a commitment. Because when you make a compromise you commit yourself to something. If you make a compromise in a relationship you are basically saying that you commit yourself to that relationship more than to your own thoughts.
If your association between commitment and compromiso helps you to remember the word, that's great. But compromise does have a lot of negative connotations and denotations as well.
It is interesting that if you look at the related verb cimproneter you find that all the positive meanings seem to be associated with the reflexive or pronomial form which makes some sense with your relating compromise with committing oneself.
Por ans para have always been one of my shaky concepts too, but it is becoming clearer. Both are used in several different circumstances, but the list for por is much longer and, to my mind, more diverse. So I concentrate on eliminating para as opposed to remembering all the functions. There are some different acronyms out there, but despite loving DOCTOR/PLACE for ser and estar, these are two bulky for me.
I think of para as an end game preposition. If you put it before an infinitive it represents a goal. Essentially it then means in order to. It also is used for destinations. Viajo por avión para Buenos Aires. Para is the destination and por is the method.
Pago por Maria.
Pago para Maria
In the first sentence, you are paying on behalf of Maria. You are the agent. In the second sentence Maria is the recipient of the benefit. You are treating her.
Here are a couple of links that might explain it better and cover more circumstances.
There are a lot of more resources out there. I used my favorite language learning search formula to get them. Just Google x vs y, in this case por vs para to see all the resources. If you want to see the acronyms Google por vs para acronym.