Southside Creations

This is something to do with defects in the drainage pipe layout. i bet you have a dishwasher as well as the sink connected to the same outlet. the greasy clumps are mini fatbergs which form because the waste doesn't drain properly. definitely not anything to do with washing stuff.

The press acts mechanically on the fitting without strain on the pipe. not sure which system you're using but that's certainly true for geberit.

What i would do is take a big breath and resign to the fact that i need to go and get the wet cutter.
except that maybe the time this will take is not considered by the tiler to be worthy of the price quoted?

Tile adhesives are cement based. if you have a concrete subfloor all you need to use is tile adhesive. don't splash out on polymer modified, extra flexible products. please don't use ready mixed stuff. buy powder adhesive and mix it on site

Yes it is. you need an integral overflow syphon. they come in all styles i.e pushbutton, lever etc.
you will need to take the cistern off to remove the old syphon and fit the new one. if you order online, make sure the base diameter of the syphon (the threaded bit that goes in the cistern's hole) fits the cistern's hole.