I am trying to see if there is any idiom or expression in Russian similar to "making it up" in English. This phrase can mean many different things, so it may be that there would be several different expressions needed to convey the same meanings.

Examples:

#1 Making it up, as in doing something to compensate for a wrong that was done

Tom spills a drink on Julie at the party and says "I am so sorry! How can I make it up to you?"

IE, Tom wants to do something to "make up for" spilling the drink. The verb компенсировать might work here, but it sounds more formal to me and doesn't really convey the same meaning. Any suggestions?

#2 Making it up, as in to do something over again, which was not done correctly the first time

Peter failed the algebra test last week, and so he must make it up next Friday.

IE, Peter must take the same test again, or take another (similar) test in order to get a better score.

#3 Making it up, as in imagining or inventing something

Ronald wrote a science fiction novel full of characters which he made up.

IE, the characters were imaginary

#4 Making it up, as in lying

Francis told everyone he saw a tiger, but in reality, he made it up.

IE, Francis lied about seeing the tiger.


#5 To make up your face, as in applying cosmetics

Tammy took an hour to make up her face every morning

IE, it took Tammy an hour to apply her cosmetics every morning

There are probably more examples of "making it up" which are not coming to my mind right now.

Anyone is welcome to suggest other examples or possible Russian equivalents of these sayings.