I think those settings are handled via bios setup but i am not fully sure. 😕

No. I Have 31 cps in my system, but only few chars in sec. in DOS Box 😒

And my Doom2 have very slow reaction on my action. FPS normal (by '-timedemo demo1' - up to 30fps), game from mouse - fast. But from keyboard - very very slow... 😒

Probably due to using too much processor. Check your task manager.

Host OS keyboard rate and delay will not affect DosBox.

I checked cps with MODE in DosBox and it seemed like 30 cps to me at the command line.

I was able to alter the rate (all the way up to 32!...max in Windows is 31!)
Unfortunately dos MODE command in DosBox cannot view status like it can in Windows, IIRC it reported status in real Dos just fine.

There is full support for keyboard repeat in dosbox, or at least there should be. But there's no program to change it. You could write a small DOS tool that issues the relevant BIOS calls, or search for a freely available tool, I guess there should be some.

As for Doom 2, look out for "Doomsday" or one of the other remakes. They use the original data files and can be made to run and look just like the original (but fast 😉 - or you can run Doom 2 in high-res graphics with lots of extra effects.