I agree with
Nonsuch that while the Celebration is official ending on September 5, it's very likely that the Parade (PtN), fireworks (
Disneyland Forever), and WoC (Celebrate) will continue to be presented well into the future (consider that the current parades - Soundsational and Pixar Play Parade - have been running for years). I think there is a good chance that the fireworks will go back to a weekends only schedule; I don't know about PtN. I would guess the end of the Celebration means the specialty foods, souvenirs, and souvie items will be discontinued. The decorations will also probably come down. I'm curious to see if the street entertainment (e.g., Dapper Dans, Fove and Dime) will go back to the pre-60th songs/costumes or will they continue with the 60th set list or will they do something new.
October is a fun time to visit the parks, but it's not really a quiet time in the parks. As mentioned HalloweenTime is very popular. The Haunted Mansion and Space Mtn both get seasonal overlays, there are seasonal foods, and some decorations (mostly in DL). There is also MHP, which is a lot of fun (side note: we don't yet know if DLR will still be enforcing the no costumes on adults rule even during MHP; the initial information indicated the ban included special events, but folks are hopeful that will change). There is a special fireworks show during MHP and usually a Halloween Calvalcade (mini-parade); last year they presented PtN, but hopefully this year they'll bring back the Calvacade.
As noted, Gay Days is from 9/30 to 10/2; it is the largest unofficial event at DLR, so expect high crowds. Like any time of the year, I would recommend getting to the parks at rope drop and taking advantage of unusually lower crowds for the first few hours in the day. If you haven't already done so, I highly recommend downloading the official Disneyland app (it has wait times, FP return times, character schedules, etc.).