Can I install Unix on my PC? I mean not Linux, nor BSD.
Although the name of this forum is Unix and Linux, most of the users seem to be running some flavour of Linux.
Absolutely, though there really isn't much reason to unless you have a specific need for one these days. The reasons would generally be that you have specific hardware/software that only supports a particular implementation of Unix. That's mostly legacy stuff these days as Linux / *BSD are the 'go to' platforms. If you decide to do this just be aware: you won't gain very much and will lose a lot in terms of functionality and software availability. Also, there isn't one Unix, there are several different vendors so you'd have to pick one.
Agree with blihp and Jeff Schaller, having done lots of consulting and managed a few data centers... when you say "Unix proper", what do you mean? AT&T system V? True64? The one true unix?
If you want POSIX certfied, that is one thing, install an OS from the list on this page. If you want to learn "unix", there is more help in installing some variant of Linux than any other "unix" out there, IMHO.
Yes, of course
I tried OpenSolaris once when it was still free. Nowadays it's not available anymore but you can still use various variants and forks of it like OpenIndiana, OmniOS and illumos. See Open Solaris derivatives and illumos Distributions
If you don't mind using a closed-source OS then Solaris 11 is still free for "developing, testing, prototyping and demonstrating your applications" as per its license. Oracle also provides ready-made VMs for use
You can find more Unix OSes here. Most of them work only if you have money though, or at least work/study in an organization that has a real Unix system