In regard to the night prayer:
1. Is it obligatory to say ‘al afwa’ 300 times, or is the person allowed to say it less.

2. If somebody accidentally misses it one night, is it obligatory on them to repeat it?

Just a brief introduction: Namaz e Shab and all the nawafils are mustahab hence it permissible to recite only surah fatiha however it is better to also recite the second surah. Qunoot is mustahab as well. In salatul witr of namaz e Shab it is better to prolong the qunoot. It is good to recite 300 'al afw' however if you recite 10, there is no problem. It is good to remember 40 believers however even one is good. Namaz e Shab is mustahab and whenever you have the strength and the will to recite it, then lengthen it otherwise recite as much as you have the strength and will to do.