I've been able to receive nearly 100% from the big guys. For folks that run their own I run into less issues these days. I'm still on Postfix. Some of the client and header checks used to (c2005) be too strict. But! When it failed, there were logs I could see.

If you run your own, you'll want to get some log checking tools to make sure things are tidy.

No issues at all. It comes down to the way they have set up their own mail servers. Incoming email is being checked for DKIM, DMARC, etc and then handled based on that. Logs are also super helpful in determining what went how in the reception process.

Yes, and yes, no problems ever with receiving mail on my self-hosted systems. exim4, self-signed cert. Sending is what may be difficult but personally I only had very minor trouble with that (VPS on a reputable provider, all set up properly).

Which VPS provider is that?

We send mail from a Linode VPS in Frankfurt, which works fine most of the time but a couple of times a year Microsoft puts us on a blacklist, most likely because of a neighbouring IP sending spam.

Hetzner. I once was blacklisted at MSFT and filled out their online form, which solved the problem within a day or two. The only provider that doesn't accept my mail (for years already) is AT&T but this is something I can live with (I rarely have to send something to AT&T, as I am only dealing with locals).