I have Italic icon names on desktop. Where I can change it? Is there any config files for this? In system settings I have all fonts set as regular. As you can see on sceenshot text file has regular font name, while program icon's names are Italic.
http://img31.otofotki.pl/ov989_screenshot2.png.html

As indicated by the bottom right icon, these files are all Symlinks.

I reported it as a bug
https://bugs.kde.org/show_bug.cgi?id=303067
I added them from right mouse click → add new program shortcut. This is all in desktop "Folder view" mode. Actually when I use Kickoff and right click "add to desktop" the effect is the same. It also creates links. Only when I add icons to desktop from Kickoff in "default desktop" mode icon's text is regular. The problem is that I don't like "default desktop" mode. Is there any configuration file where font style for links are set?

As far as I am aware, there is no configuration in this case.
Symlinks are preferred in this case - as installing updates system wide will update the icon.

I created my own shortcuts on my desktop

Example For Dolphin window manager:
First Delete dolphin shortcut from desktop, then
Open Kate text editor,
Paste this:

[Desktop Entry]
Icon=system-file-manager
Name=Dolphin
Type=Application
Exec=dolphin %u

Save as Dolphin (without .ext), choose save nevertheless
Double click ->
click continue (will be asked only once).
Kaboom there you have an icon with regular font and without the shortcut arrow.

I have a related issue. The text labels on my desktop icons are in a font & colour combination that I find very difficult to read. I've tried every config tool I can find in the interface, done many web searches, and gone spelunking in config files, both in my home directory and the KDE system directories, but cannot find any way to change the font.

Changing the 'Global Theme', 'Plasma Style', 'Application Style', 'Colors', 'Fonts', and/or 'Icons' settings in the "System Settings" window has no effect. There is no option in the right-click, "Desktop Folder Settings" -> "Icons" dialogue to change the font or its colour or get rid of the shadow stuff around the letters.

I would included a screen shot of the problem, but I'm not finding any link or button in this forum interface to attach files.

OS = Open SUSE Leap 15.2
Kernel = 5.3.18-lp152.41.1
KDE = 5.18.5-lp152.1.3
Plasma-framework = 5.71.0.lp152.1.1
Plasma5-desktop = 5.18.5.lp152.2.1

My last resort will be to copy the icon image files, edit them to include a readable label as part of the image itself, and then turn off the KDE icon text labels, but that seems like an extreme measure.