Printing Errors or Lights & Stuck Print Jobs

I made the mistake of installing the HP software because the MacOS automated system didn't seem to pick up the right driver (I also use a multifunction printer).  Now I get plagued by frequent ink popups that basically tell me that I have HP cartridges (which I already know, thank you) and for which I do not seem to have a means to kill them off permanently.

Worse is that it's not just ONE pupop but about 4 which then vanish again, and they take focus so it makes a mess of whatever I'm doing when they appear.

How do I (1) eradicate these popups in full, completely and in a manner that ensures they never appear again, (2) ensure that the next driver update doesn't re-introduce them and (3) get the [redacted] sacked who came up with this [redacted] idea?

In general, I would also like instructions on how to completely eradicate HP drivers from my system - there seems to be a rather high element of data extraction to be embedded in both the software and the printer which runs diametrically counter to our ever increasing privacy needs (like the soon to be introduced EU GDPR legislation which can cost us as much as 4% of turnover if we make mistakes).  If we do not gain control over this we may have to abandon our use of HP printers altogether.