Blocking someone actually opens up a sub-menu where you can “check” block messages, block games, or both. Feel free to test it out, you can again cancel these blocks the same way. It does not affect friendship nor group requests unfortunatelly.
Regarding the friend and group requests, HHG is correct, let me just elaborate on it a bit. On any requests, there are two big buttons (accept/decline) and a small “ignore” button on the top right.
Clicking accept or decline lets the user know what action you took and he/she/it/them (just read the gender pronoun thread 
) can invite again. There is no limit on subsequent requests that I know of. If you click ignore the request will never bother you again. But you cannot be re-invited for the friendship nor group, so carefull about that :). I actually think it is not fully intended, but works in your favour sometimes.
And if you suspect the user is being intentionally annoying, it never hurts to report. 