If you can see SD2's gui and hear the hits when you click on the drumkit picture you actually are almost there.
Hitting the picture does not output MIDI to Reaper, so you can't record your "mouse-drumming" on those pics. That's normal in any vst host.
If you want to program grooves from scratch with nothing but the mouse you insert an empty MIDI item, open the MIDI editor for that item and click-insert notes in the editor like you would with any other MIDI instrument.
Different pitches stand for different parts of the kit with MIDI drum instruments, so you benefit a lot from downloading a note name file to load into the MIDI editor, then you can see by name which key sounds which instrument. Go to
the MIDI drum map page of the Reaper Stash to find one fitting to your drumkit. I think SD2's standard kit would be the one called Superior 20 drum map.txt.
Of course you can also input grooves with a MIDI keyboard or better some drumpad controller. Or use the MIDI groove loops that come with SD2.
As of the latter, I think SD2 comes with EZPlayer as an extra plugin which you can load into a slot
before (upstream) SD2 in the same track's FX chain. You need to click on the "MIDI" button on EZPlayer's window header and set MIDI Output to "Merges with MIDI input" to make the two work together on one track. Save that FX chain, so you don't have to set it up again in the future.