From the 2008 rulebook (I haven't checked the Fastracks to see if anything changed...), DSP lists:
Civic Si DOHC VTEC (‘99-’00)
Civic SOHC VTEC (’92-’95)
Civic VTEC, SOHC and DOHC(’96+)
FSP lists:
Civic (‘92-’95) NOC
Civic (‘96+) NOC
A 92-95 VX/CX would fall under the FSP listing. "NOC" = not otherwise classified. Since the Si was already called out in the DSP listing, NOC catches all the other models for that generation. You would be limited to engines from non-Si 92-95 cars, no K20 obviously.
For your 2nd question, the update/backdate rule only applies to models "on the same line". So while the 92-95 Si is in DSP with Civic models from various years (including the current K20 powered ones), it is not on the same line. So you'd be limited to D16Z6 power only.
The first class legal for a K20 EG Civic would be Street Mod.