- can microscopic particles of dirt in the groove become more audible making older albums sound worse?As a rule, finer profile styli are quieter in the groove than larger, coarser styli.
- will a stiffer stylus make skipping due to scratches more of an issueThe stylus won't be stiffer. For LP playback purposes, all diamonds are equally stiff. The cantilever and/or a rebuilt suspension may be stiffer. If so, that may increase the likelihood of skipping. It will also affect the rise time and amplitude of signals generated by groove modulations. Whether for better or worse depends on the system and listener.
All that said, the best/first answer is, clean your records and replace the badly scratched ones. There's no reason to play dirty records. The only reason to play a badly scratched one would be if it were some irreplaceable rarity (in which case you should at least clean it properly).