I just installed Silver and the installation went through without hickup, but when I try to run 'start.sh' under 'GOG Games/Silver German/', it just fails with

Running Silver (German)
./silver_launcher.sh: line 1: ./silver32: No such file or directory

And running 'silver_launcher.sh' under '/game' just produces the same error, even though it's clearly sitting right next to the 'silver32' exectutable.

What gives?

I'm running a bit of an exotic system (CentOS 8), but that error seems weird.

Does your OS support 32-bit binaries at all? Do you have 32-bit ld.so installed? What do you get with "ldd silver32"? This sounds like a CentOS/RHEL question, which I am no longer equipped to answer.

ldd silver32 just gives me

not a dynamic executable

Which sounds kinda wrong. You might be correct on the 32bit issue. Supposedly RHEL/CentOS does support 32bit, but apparently not out of the box…WTF? Anyways, apparently I need to install it manually, but there's no straightforward guide for it, since gog obviously cant talk to dnf to solve the dependencies. Oh well, back to the 90s, I guess.

Still, it's a kinda weird error, assuming it's the 32bit problem.

So it's indeed a 32bit issue.
After installing 'glibc.i686' which is one of the main packages for it, the starter at least gives me useful errors, telling me which libs it's missing.
Problem is:
The listed libs are all written down in ubuntu/debian notation and CentOS (and thus RHEL and likely also fedora) call them differently.
So far, with

dnf install
glibc.i686
libglvnd-glx-1:1.0.1-0.9.git5baa1e5.el8.i686
SDL2-2.0.8-7.el8.i686
libstdc++-8.3.1-4.5.el8.i686
mesa-dri-drivers.i686

I can get it to kinda start.

I say "kinda", because nothing happens for a while, but my mouse starts flickering and is glued to the center of the screen. AFter a while, I get some ghost windows popping up and vanishing and a bit later, a get a screen filling, black, "silver" window, but nothing happens. After crtl+c'ing silver, I kills part of my window manager and locks up my machine, and a few minutes later, it recovers, as if nothing happened. And Terminal output is not helping. Weird.

Not on the 'net often enough lately to keep track, but yeah, this pretty much means missing ld.so. ld.so is the one that gives you more informative errors; if it's missing, you just get weird stiff like the missing file (meaning missing ld.so, but it doesn't tell you that) and not a dynamic executable (meaning the 64-bit ld.so didn't understand it).

edit: as to your other issues, I personally just use wine with the Windows executable, since the Linux executable for Silver isn't really that great. I haven't run it in a while though, so maybe after this COVID-19 panic shutting half the city down, I'll have time and opportunity to retest.

I tried run this game in on Fedora 32.
Install nex packages:
mesa-dri-drivers.i686
mesa-libGL.i686
SDL2.i686
glibc.i686
libstdc++.i686

Game has started, but i have black screen. Not sound, not mouse only black screen.
Have idead how fix this problen?

I know this is old, but Loom is a ScummVM game. I installed it, but ran it using ScummVM. You can also install it using Lutris and it will correct the issues too.