The system I have is not a regular PC. It is a "put together" or "setup" of some left overs from old PCs:

The motherboard:
G45T AM2 V:1.0
Manufactured in 2007, Acer Aspire M5700's motherboard, running Windows Vista.

The CPU:
Intel Core2 Quad
This is the CPU Acer aspire M5700 used to rung Windows Vista.

The RAM:
Apacer DDR2 800 SDRAM 4G (2G x 2 sticks)
Bought from a 2nd hand parts store 10 years ago and used for running Windows 7.

The PSU:
Corsair RM650x
Only its 24pin cable, CPU cable, and optical drive cable can be used, other cables can not be used because of the loose connections which might causing damages.

The GPU:
On board Intel G45
The G45T motherboard has its own on board GPU.

The BIOS:
American Megatrends V.02.16
This is on board of G45T AM2 V:1.0
It's never been updated and do not know how to update it.

The CR2032:
New. The only part new.

Flash sticks:
One, HP c330 w, a 4GB USB2 flash stick. This is the Xfce USB live bootable running now.
Two, ADATA 16GB USB2 flash stick. This is the flash stick on which Mint will be installed.

The above said parts are put together on top of a wood bench, without a case.

My questions:
1. Is the system as said above able to run Mint?
2. Have learnt that Mint has three editions, Cinnamon, MATE, and Xfce. Which one of the three can tolerate and run on the system as said above?
3. Can any one of the three Mint editions be installed on a USB flash stick, 16GB USB2, ADATA brand?

Thank you.

It's not the distro that puts demands on the hardare: it's the desktop. Most distros come with a default desktop but you can always use a different one if you prefer. Of the three Mint editions, Cinnamon is the heaviest default desktop so I wouldn't use that one on your system. Try one of the others and see how it runs. If it's still too slow for you, switch to a simple window manager like fluxbox or ice. These don't by themselves provide desktop icons but you can add an icon manager for that, or just use the menus. Linux is about choice.

You can definitely try to boot almost any distro from a pendrive and you will see the result (if bootable). You can try to install them ony any hardware, but I think 16 GB is not that much. It depends on your needs, a KDE or Gnome desktop will not work very well.

Adding to the excellent advice given already, and assuming you're talking about a desktop,

1. Yes, though browsers are memory hogs. You could have / on one stick and /home on the other.

2. Of the three XFCE is the most customizable, but for many situations you can get by with just a window manager alone and skip running a heavy desktop environment as mentioned. The Desktop Environment and the Window Manager are optional, separate, replaceable layers. Openbox is popular. I'm partial to the FVWM-crystal WM even though modifying the menus means firing up a text editor (graphical or not) and knowing which files to edit.

Applications are also interchangeable, in principle. It is a matter of supporting the standard protocols for networked applications and the right file formats for others. So there are a few lighter web browsers than Chromium and Firefox, though they will lack in some areas. Likewise, there are a few lighter productivity suites besides LibreOffice, as well.

3. Not too many years ago, only a few gigabytes was enough even for a desktop. The latest version of Linux Mint (21.1) requires 16.1 unfortunately. So the short answer is "no", at least as far as desktops are concerned. I blame "snaps" packaging for that.

However, you could try an edition of Ubuntu, such as Lubuntu, and add or remove what you like until it is about the same as Linux Mint. Linux Mint is derived from Ubuntu anyway. Or you could start really bare bones with Devuan or Debian or Alpine, and then add in only the pieces you need.

That's actually a very good piece of advice if you don't mind getting your hands dirty. And as you've put together your own hardware, you should have the wit to do the same with software! Debian/Devuan have a form of installer called net-install. It installs a barebones system that you connect to the internet and then continue online. I did this many years ago when I knew a lot less about Linux than I do now and I found it easy and very useful. Add xorg (the graphical server) to your system, then a window manager of your choice (several good ones have been named here) and finally your desired applications.

The Debian family lend themselves very well to this kind of installation because whatever you install brings its own dependencies with it and will work out of the box.

I also agree that debian or devuan would be a good choice. I have a debian virtual machine that uses about 12 GiB of space with about 2 GiB of user data. However, running from an installed USB will not be as fast as the live version or an internal drive and cheap USB drives are not going to be long lasting.

Thank you, Gentlemen.

The date on which I first touched Linus was December 5, 2022, downloaded Linux Mint Cinnamon edition, 32bit, made it a USB live bootable on a flash stick, and tried it for a few days. Then, tried Puppy Linus BionicPuppy32 amd 64, and FossalPup64, and other Puppies for about 2 weeks. On December 20, 2022, I found LXLE on Google Search, it was saying that LXLE is light weight and most friendly to old computers. I made it a USB live bootable on a 2GB slash stick and ran it every day for about 6 weeks. I like it. But had too many questions but found no answers. Had to give it up.

I said in my previous post that I am just a first grade pupil. Thank you very much, Gentlemen, for trying your best to help me. It is a shame on my part that I do not understand what you are talking about although I can read your words. I cannot reply to anyone of you, simply do not what to say. Thank you, Gentlemen!

(A point of information: LQ remains a co-ed community.)

If getting a beginners' start is necessary, then you might put Lubuntu at the top of the shortlist.