Everything there looks fine. The unchecked entries are Source Code.
So it does install without trouble in Live Trial mode, but not on the Bare Metal Installation?
Yes. From CD no problems. But on installed - can't install. Very strange.
I have tried to write all conflicting packages to install and have gotten this. I think it can be useful to find the source of the problem
Please Do Not attempt to install i386 packages. This can break Zorin OS and is unnecessary to do.
The packages needed for 32 bit support are in add the 32bit architecture and in wine32, not in wnie32:i386.
So what should I do?
Have you visited the WineHQ forum?
Yes. But it doesn't help
Can you try...:
sudo apt remove --purge wine
sudo apt clean && sudo apt autoremove
sudo apt update && sudo apt install lib32z1
sudo dpkg --configure -a
sudo apt full-upgrade
sudo apt install zorin-windows-app-support
If the above fails, let's try installing from the Wine Repository step by step.
Going to wine repository
This looks a lot to me like a Libc6 bug.
What version of Libc6 do you have?
ldd --version
It also looks like Mirrors disagreeing with eachother as to which packages to install.. So I Must Ask...
Have you Run all of the commands I posted above?
Are you certain that in Software & Updates, you are set to Main Server?
May I ask you to send me output of
sudo apt edit-sources?
deb http://archive.ubuntu.com/ubuntu focal main restricted
deb http://archive.ubuntu.com/ubuntu focal-updates main restricted
deb http://archive.ubuntu.com/ubuntu focal universe
deb http://us.archive.ubuntu.com/ubuntu/ focal-updates universe
deb http://archive.ubuntu.com/ubuntu focal multiverse
deb http://us.archive.ubuntu.com/ubuntu/ focal-updates multiverse
Not helped. 
Under "Other Software"
Is CDROM: Zorin unchecked?
Yes. it is UNchecked
Ok... I still think it is the libc6 version... let's get risky.
sudo apt install libc6=2.31-0ubuntu9.2
This will want to REMOVE a bunch of packages like:
build-essential will be removed
g++ will be removed
Please post that output here.
That makes two of us...
That should be the focal package...
Let me go look...
sudo apt install libc6=2.31-0ubuntu9.2 libc-bin=2.31-0ubuntu9.2
Perhaps Aptitude can handle it?
sudo apt install aptitude
sudo aptitude install libc6=2.31-0ubuntu9.2