How did Charlemagne become a rival to the Byzatine
emperors and the Abbasid caliphs?

He proclaimed himself as the Holy Roman Emperor and spread his territory in all directions. While doing that he enter into quarrel with these two countries.

Explanation:

Charlemagne proclaimed himself as an emperor in 800. Until then only rulers of Byzantine Empire had that title in Europe. They didn't accept this, especially as Charlemagne proclaimed himself as the successor of  Roman emperors.

Abbasid caliphs fought with Charlemagne as he tried to take their territory in Spain.

are their options?

otherwise i can't

the best description of postwar writers might be progressive.

following the war, writers showed a tendency to work on artistic or social matters rather than political themes. while postwar literature may not have been the greatest period of english literature, the themes provided excellent critics a high number of novels. such examples include anthony burgess, anthony powell and frank kermode, all of which can be placed under the progressive view.