Converts atmospheric nitrogen into ammonium, which plants absorb. the plants, by incorporate the ammonium into proteins. ammonification, nitrification; nitrogen fixation, assimilation; assimilation, nitrogen fixation; or nitrification, denitrification? which one?

The answer is Nitrogen fixation, assimilation.

Plants are not able to directly use atmospheric nitrogen. It must be converted into different form through a nitrogen cycle. In the process of nitrogen fixation, nitrogen fixing bacteria converts atmospheric nitrogen into ammonium. In the process of assimilation, plants incorporate ammonium into proteins.
The next steps are ammonification, conversion of organic nitrogen from dead plants back to ammonium; nitrification, conversion of ammonium to nitrates; and denitrification, conversion of nitrates into atmospheric nitrogen.

Gay-lussac's law i think.