1. Does depressing the CMS switch have a function in the R/L F-16 and what blocks are we talking about?
No function, regardless of block. I guess they designed the switch thinking on adding something and then when the software was done they couldn't think of any use for it.
2. When Googling I found multiple Falcon 4/BMS related tutorials all confirming what is said here: UP: either 1 to 4, LEFT: 6, RIGHT: put to SEMI/put to idle, DOWN: consent in SEMI and AUTO modes. However, does it work exactly like this in R/L too? Do we have anything to back that up?
Until recently we didn't, because it was classified. Currently, we do, in the form of what I understand is an F-16... mechanic? (maybe) with access to the real manuals. Don't remember exactly but I think it was the user Dee-Jay or Mav-jp over the BMS forums... hmmm... don't remember the name really.