The numbering system was reset in 1962 as part of a bigger change, unifying aircraft designations across all the service branches. Some aircraft designated prior to this kept their designation, while others changed. Soviet aircraft obtained by the US for test and evaluation were often given designations >100 so they could be referenced internally without giving away what they really were, as the evaluation program was classified.

As for the F-117; fighters are generally regarded as sexier and more attractive than attack, bombers, cargo or other types. By calling it a fighter the USAF reckoned that recruitment would be easier and also that it's real purpose would be obfuscated. This is also the reason for the number; by giving a high number they indicated that this was an airplane designed prior to 1962 which never became anything.