Juha--you are the KING of asking a large number of totally disconnected questions in a single post!
To address the title of this post, "Compression taking place", and, I'm assuming, your primary, core question:
PureSignal has NOTHING to do with the compression you see with your amplifier.
Audio processing has NOTHING to do with the compression you are seeing with your amplifier.
But it is great that we have AmpView to help us recognize it is happening.
What IS happening is that, for whatever reason, the design of the amplifier has more gain on 20M than it does on other bands. Therefore you must lower your drive level to keep it out of compression. It's that simple. And it has nothing to do with anything other than drive level. Of course PureSignal will help this by effectively reducing the drive for you, but you will get better performance by making a gross reduction in drive so PureSignal doesn't have to work so hard.
As for your other questions:
2. While re-reading some many threads on PS, I came across mention of the "TINT" parameter that I can see on the Linearity form. I don't think that I have ever changed that, but it reads 1.1. In one thread I got the idea that having 0.5 in the TINT box may work better, but again, I have no idea what TINT actually does so why 0.5 would work better or not isn't very clear to me.
Yes, you want TINT to be set to 0.5dB. It will work better.
You can actually blame that all on me. I asked Warren to expose this adjustment with the idea that it might be helpful in certain situations. AFAIK it never has been. You can read more about it at the main, tacked, PureSignal post which I'm sure you are familiar with:
viewtopic.php?f=20&t=3166I strongly recommend you change this back to the 0.5dB default.
3. Another thing that was mentioned in another thread was "Single Cal" that I may want to experiment with although I thought that this is a sort of "one-off" feature after which NO continuous auto-calibrating takes place until I hit "Single Cal" again", I am not sure if I got this right

. In fact, I have NEVER used it. For PS, I use the 2 TON button to "auto-calibrate" for each band (I do that again when I bounce from one amp to another and/or if I build another antenna for a band) and not mess with PS after that.
Unlike TINT, Single Cal is often quite useful. If you want PureSignal to make a single measurement and correct based on that measurement this is the way to do that.
It is more often used with two-tone. Assert a two-tone test signal, normally done at your full drive level, and then hit the single cal button as many times as you like until you see a correction you like. Then don't mess with it. You'll notice the PS-A (automatic) button turns off. That just means PureSignal is no longer in automatic mode, not that PureSignal is deactivated. You also don't see a correcting indicator, which is probably a bug, and a bit disconcerting. But you can see that transmitted IMD is low, so obviously PureSignal is still running.
So why might this be useful? I find it most useful during digi mode operations where I don't want PureSignal to be making any corrections or changes during, for example, a long FT8 transmission. So after tuning to the dial frequency I want, I make a transmission, fire off a single cal, then operate digital with low IMD. Another example might be if you are seeing occasional "blow outs" for some reason you can just hit single cal and then PureSignal won't have any opportunities to "make a mistake".
4. I also read that one may want to play with the Max Gain of the Leveler (mine is set at 5dB) as increasing that number may help the CFC when using PS. I have also heard that increasing the Max Gain of the Leveler beyond 5dB wasn't a good idea (that discussion had nothing to do with PS if my memory serves). However, I have some compression applied even before the audio from the MIC even sees the ANAN so I am not sure if increasing the Leveler Max Gain would help. Or, perhaps, I reduce any pre-ANAN compression (I usually don't run a lot of compression) and make up for the reduced compression by increasing the Leveler Max Gain dB figure.....
This question has nothing to do with PureSignal. Increasing leveler max. gain will not help, or hurt, CFC, assuming you do your part and ensure internal levels remain below 0dB. The leveler is merely another type of compression stage, just like you apparently have some compression going in your DAW prior to the leveler.
How much compression you use, what kind of compression it is, and where you use it is a very personal decision and depends very much on the characteristics of your voice, how you use your microphone, and other intangibles.
IMHO the three stages and types of compression available in Thetis, the leveler, CFC, and ALC, are more than enough by themselves and no external compression is required. (I don't count COMP or CESSB because they are, IMHO, obsoleted by these other compression stages.)
As a rule of thumb, most people do quite well with 5dB of leveler gain. To use myself as a corner case, my leveler is set to 15dB and 100ms decay, which is quite aggressive. But while I get great signal reports like this when others have tried it the results were not desirable.
So you will have to experiment, there is no single answer.
5. ALC Comp is hitting 3dB (even 5dB) at times when I transmit. Would I do better to switch the meter to ALC Group and hit 3dB at times?
Again, this question has nothing to do with PureSignal. And it has nothing to do with the extra gain your amp has on 20M.
ALC Comp and ALC Group meter modes read exactly the same when ALC is in the positive numbers. ALC Group meter mode is merely a composite of the ALC meter (which only reads to 0dB) and the ALC Comp meter (which only reads above 0dB), i.e. it's a convenient way of looking at all ALC data on a single meter. You can safely, and conveniently, use ALC Group in place of the other two meter modes.