Call me mister suspicious if you like but I have had this exact issue daily with Chrome since they started complaining about adblocking. And wouldn’t you know it, the moment any form of adblock is disabled it miraculously does not happen. I can also fix it by clearing my cache every day and restarting the browser. I would start with those steps.
Bit of both really. Ok, the bed tramming is normal, even GREAT printers need it done every few weeks or so. The physics and mechanical properties of how the bed is held down mean changes in temperatures and normal shifts even in an ACed house mean they loosen naturally a little every day and after a few weeks they will be bad enough someone who likes a really level bed will need to clear them again. After a few months any bed that isn’t welded down is going to need to be redone.
Z offset and bed auto level follow from that. You need to redo them when you do the tramming anyway.
I would say run your printer more often but that won’t fix it. You’re running against physics and nothing can stop that. Maybe you can store up prints for say 6 months and then do them all in a week or so and you only have to do this once?
The piece probably left the build plate and stuck to the nozzle, got pushed in and melted. OP got lucky and it didn’t hit anything hard and cause his leveller to break.
You can’t slow down the head in specific spots but you can slow it down in general as well as setting a minimal layer time so that it pauses between layer and lets them cool.