I'd like to know if codegolf does allow other kinds of challenges, like memory-size related ones (Given a structure, try to use the least amount of bits to store the same information) and so on. I don't know if this kind of challenge fits codegolfing or not.
There are two different usages of "code golf" here:
The tag code-golf is applied to challenges which involve competing to produce the shortest valid source code. More details and a list of challenges can be found by clicking on the tag name.
This website, "codegolf.stackexchange.com", has the full name Programming Puzzles & Code Golf. This site has several different challenge types, code golf being just one of them.
Sometimes people post challenges that have their own scoring method that does not fit exactly into one of these categories. These are tagged code-challenge, and the challenge post contains a detailed description of how submissions will be scored.
We also have non-challenge questions, asking for advice on solving such challenges. These are tagged tips.
From the code-golf tag wiki:
Code-golf is a competition to solve a particular problem in the fewest bytes of source code. If you want to score by characters instead of bytes, state this explicitly in the challenge. If source code length is not the primary scoring criterion, consider using another tag instead.
So, no, code golf is solely about code length.