Alright, utilizing the gpt fdisk which first had to be downloaded and installed, I went ahead and finally ended up duplicating my existing sda partitions to the external 4TB SSD drive. Silly me hoping that the cloning process would stretch the new partitions accordingly, but of course nope, just created identically sized partitions on the new sdb disk. No problem, we'll worry about resizing things later. At least now it looks like I'm starting to get somewhere.

Using:
I then began formatting the largest of the new partitions on sdb which happens to be 1TB in size. This began well over an hour ago, so I hope that everything is still A - Okay. Here's the output of that:

So now I have 4 duplicate partitions from my current primary sda which were created/duplicated with gpt fdisk on sdb, ranging in size from 1TB down to only 16GB in size. The 16GB sdb1 is going to end up as a swap file, but we'll concern ourselves with that partition later on or tomorrow, depending on how well the current process works out. I began with the current 1TB formatting around 3:40 PM my time (Germany). It is now 5 PM so the formatting process has been going on for an hour and 20 minutes already.

I would not expect formatting 1.6 TB to ~1.3 hours. Formatting does not actually clear data just create the metadata and journal. I am wondering if you messed something up with cloning. Your old disk used MBR. Did you clone the entire disk or just individual partitions?

Using gpt fdisk I only duplicated the partitions without the data. There was a message stating that it recognized the 2TB sda as having an MBR and that that would be temporarily converted to GPT and stored in memory. After that I got the success message that the partitions were created. Then I used fdisk -l to check and all of the partitions that I had on sda wre now also on sdb, but without any actual data.
After that I began formatting one of the actual partitions on sdb.

Now it's 6:50 PM my time and it's been formatting this 1TB partition for 3 hours and 20 minutes. Yup, I'm beginning to think that something is not right. Will let it run another hour or two and then I'll break it off ....

EDIT: After 6 hours and 30 minutes I terminated the terminal window since I couldn't get it to stop any other way.

Something went afoul but I don't know what at the moment. I would start over by creating a new gpt partition table (don't copy), create the desired partitions and then format.

Anyone familiar with the program Penguin-Eggs?
If you could make an installable image of your system with the clone option, install to the SSD drive using the partitioning and initialization software in the installer......

I wonder if that would work?

This is just mind-boggling madness to me. I have never since I've been using Linux (2009) encountered such problems with MBR as I am experiencing for attempting to get a 4TB disk working the first time. It's just driving me sheer nuts at this point. When you look at the wiki pages they tell you what happens when some command is being utilized, but nothing seems to be complete and/or written in a plain understandable manner. I have never had a problem with MBR drives up to 2TB and I' ve never (contrary to other users here) have experienced a problem with Gparted ... until now.

I create the partition table with gdisk.
Then I wish to create the first partition.

PROBLEM: The WiKi tells you how to create, how to copy, how to save, and how to restore a partition table. The WiKi alsop tells you how to *BEGIN* creating a partition. I write *BEGIN* because as soon as you select the command for making a partition the question arises for the first and last sector options.
Okay, first is easy enough, that's either 34 or the gdisk default. But how the heck is a person supposed to determine the last sector if the desired partition is supposed to be 225 GB in size?
Furthermore, even if I wanted to make the entire root of the disk one partition, how do I determine what the end/final sector is? That's where I get an error message that the selection is out of the boundary confines ... even though it's a sector number that gdisk is showing me on the screen. At this point I'm about ready to throw the computer or the drive out of a window. How can this be so confounding ???
(sorry, just really really frustrated at this point)

Here's my output from the last attempt. Creating the table no problem. Writing and saving GPT to disk no problem. Creating size for a partition asks me to choose either "B" Bytes or "M" Megabytes? or "G" Gigabytes or "T" Tetrabytes? or "P" for Petrabytes? So I chose 225G in the +size command.
This process completed successfully as you will see below.
But then when I checked the final output afterwards, I had a partition size of 500 *BYTES*
Checked that with Gparted and confirmed that it was indeed 500 Bytes.

And before someone tells me that I should not have entered 1 for the command including +size 225G behind that, then please refer to the WiKi pages because that section for properly using that command lets the user guess as to the correct input. I didn't think that 1 225G was correct, so I used 1 +size 225G, assuming that +size meant ... telling gdisk to add a size, specifically one that's 225G.

I do not know what I'm doing.
Most people who purchase a larger drive would not know what they're doing either.
And that's why *SIMPLE* step by step instructions for all of us millions of dummies are so important.

Isn't there some way to split a drive into pieces (without a hammer) before a partition table is applied? If I could split this drive into three then I could just continue using MBR as I have been for decades. And then I wouldn't run into any Gparted issues either (methinks).

You appear to not be asking for your preferred size correctly (225GB)

When you get the prompt for 'size' try entering +225G

(Usually, if you want the rest of the drive as one partition, just press enter.)

With all the trouble it might be a faulty drive. Yes I’m aware it is a new drive, however it wouldn’t be the first time something was sold broken.

Yes, I'm beginning to believe that the disk is fault or bad. Creating a GPT partition table has never been a problem and using parted or gparted has never been an issue for me in the past until I bought this 4TB Samsung Evo. The commands all check out or at least I never see any errors. Just like the last commands that I tried. First I created the GPT partition table followed by creating a 225 GB sdb1 partition. Got out of parted and commenced with the following which also should have been no problem if everything was working correctly.

Yet it's been "formatting" this 225 GB ext4 partition for over an hour now.
So clearly, something appears to be wrong here.

PROBLEM SOLVED !!!

Apparently all along the issue was the fact that I was attempting to do create the GPT partition along with everything else on an external 4TB SSD disk. I'm not sure if it was the external controller that's at fault or just the fact that this wasn't meant to be done on an external disk, but whatever the case .... I went ahead and got an older backup / emergency setup of mine, took the disk out of that one, then installed the 4TB SSD Samsung in that system as the primary. After that I booted into my own custom Live MX without a problem. Just for sh**s and giggles decided to go with gparted since that's always been my goto for the past 10+ years .... and voila, 10 minutes later I had GPT installed along with formatted partitions.
It just never made any sense to me that gparted had any fault in that situation.

I was trying to get everything done on my regular setup since I only have one display at the moment. So changing to a different system with a new primary disk just seemed like a pain in the rear. Had I done that to begin with, this post wouldn't exist.
Sorry about that.

There's still one more related issue but this is not the post for that. I'll write another post on that one, having to do with the EFI boot partitions. Anyway, off I go. Thanks for all of the help here, I really appreciated it.