Sony updates are available on the customer support pages - but there don't seem to be any for that model any more.
OTA updates were discontinued years ago, in fact the entire service no longer even exists (it was a VERY expensive way to do updates).
However, it seems VERY unlikely that the set would require a software update to fix the issue - unless QVC have made some bizarre changes to their broadcasting specification - and even if they had, it's highly unlikely that Sony would reassemble a team to rewrite the sets software to cure the issue.
The tuning issue sounds like you've probably tuned to the wrong transmitter?, auto-tune very commonly does this, as it usually simply selects the first multiplexes it finds, regardless of strength or viability. The correct ones are usually stored up in the 700's 0r 800's, so you could try looking there, and confirm that they are.
You then have the option of manually moving the channels to where they should be, or manually retuning the set - and best to do a factory reset first.