General

52% would be the lowest score (without rounding the decimal places). (91+91+86+52+100) / 5 = 84%. I think.
mehhh idk, too lazy to think.

so is it 83 then?

Mode of 91 implies that there are at least two scores of 91, given there are no other repeats. Median of 86 implies that there is a score of 86, two scores larger than 86 (the two 91's) and two lower scores. The sum of the scores is 5*84 which is 420 then you subtract the known scores...you get 152. To get the lowest possible score, while having 86 be the mean, subtract 85.