So sorry for the challenges you're having. First, I am surprised to hear your description of the 7570, after 13 years mine (well, not mine, gave it to DD for her birthday in October) still purrs, quiet and smooth. Did you keep yours well cleaned/oiled/serviced? I worked for the dealer for many years and never heard one of these sound anything remotely tractorlike but ya never know.
Regarding the new machine, if none of the factors such as damaged foot, misalignment, tension issues etc. was disclosed I would act accordingly - report to paypal if you paid that way, try and resolve with seller first, go through your cc company....
That said, should you decide to stick wtih it it sounds like it could use a good thorough going over/service by an authorized dealer, particularly on the tension issues. The default tensions are always recommendations and you can adjust, I would try doing so to see what diffence it makes - i.e. if the default tension is 3, take it to 2 or 1.5 and see what happens. Keep samples to take to show dealer with settings marked.
As for the thread cutter, well.... it was tempermental on the 2140. It can be adjusted. I have just sold my 2144 but never a problem with the cutter - Pfaff improved it on the 2144/70 (the update from 2140 to 70 did not adjust for the cutter, that was a hardware not software change). But occasionally if it didn't cut perfectly I would know that I just hadn't cleaned out threads -- just using the brush to brush out lint/little bits of threads that may be in the cutter area that it's cut is essential to consistent clean cutting. Many 2140s needed cutter adjustments though and you can have that done at the dealer.
I can't help with the tapering... may get the manual out later but it's not nearby, I just never used it after learning so sorry can't offer up tips off the top of my head. But which specific stitch was it you were trying to taper