Can I still load this file into the camera which now has the new firmware?
Almost certainly. While the saved settings file is stored in a binary format, it is backwards compatible with the firmware versions for the same camera model. If there are new settings or options that Nikon made available in the updated firmware, when you apply your saved settings from then
.BIN file, the new options will just have their default settings applied.
I have updated firmware on several Nikons (D500, D800, D750, D3) several times, and have never had any problems re-applying my saved settings after firmware update.
If not, can re-install firmware 3.11 to replace 3.12?
Unsure. Searching around, there are lots of anecdotes saying this has been possible for at least some of Nikon's DSLRs for several years. There are also lots of statements saying that the camera won't allow you to downgrade firmware.
This discussion at dpreview.com shows a responder suggesting to try to install an older firmware on a Z-series body, but the original poster replies that it only recognizes newer firmware to install:
Have you tried loading the older firmware file? (uncompress file, place binary in card, insert in camera, update from settings page)
It seems it only [recognize] newer version of file.