I think it shows all support units available up the command chain, as far as STAVKA. For some reason it also prioritizes the choice of support units higher in command (example: if you have a sapper regiment in army command and also in STAVKA, when you assign a SU sapper unit to a cav corps, the game will choose the one from STAVKA, not the one from the army) - or is it random? It happened to me on several occasions, but Im unsure if on 100% occasions
Also bear in mind that you cant assign several types of units to a corps, mainly artillery (even the ones named Corps Artillery Regiment!)
And finally, yes, you cant create SU from the corps screen, you have to create them in a HQ screen.