On the page we get the unread replies from threads we posted on , are we supposed to continue receiving the threads listed even If we delete replies from those threads ?
AFAIK, no.
I'm aware that we are able to stop receiving them If we remove them from the watchlist.
Untrue. Watchlist and "Show new replies" are not connected and the latter will continue to persist and show you replies regardless of it being on your watchlist or not. The watchlist could be considered as a personal filter, to look at threads that you want to actively be updated on while the "Show new replies" section is for past discussion you may have been a part of.
