If I want to copy/paste something to/from a register I have no problem.
For example if I'm in Visual Mode and I press "ay the selected region get correctly copied to register a (and if I press "ayy in Normal Mode, the line under the cursor get correctly copied into a).
During the sequence I can see the characters I pressed in the bottom bar.
If I try to hit one of the sequences "*yy, "*dd, "+yy or "+dd, when I press the double quotes they appear in the bottom bar, but when after this I press * or + the sequence in the bottom bar disappear and if I complete the sequence, it doesn't copy anything to the CLIPBOARD and PRIMARY selections.
System: ArchLinux
Window manager: suckless DWM
Terminal: bash on suckless ST
You're missing +clipboard support in your Vim.
On ArchLinux, you can get a Vim with +clipboard support by installing the gvim package.
See Vim Installation on the ArchLinux wiki, more specifically this note:
The
vimpackage is built without Xorg support; specifically the+clipboardfeature is missing, so Vim will not be able to operate with the primary and clipboard selection buffers. Thegvimpackage provides also the CLI version of Vim with the+clipboardfeature.
The gvim package will include a new gvim command for a GUI version of Vim, but it will also include a regular console vim command, only that one will have support for +clipboard when running inside a terminal attached to an X11 display.