Hello Haseen,
1) The FINAL APP (blue) mode which is armed. Similar to GS (blue), no FCU action is needed, once all self-activation prerequisites are met.
2) Yes, not exactly what you describe (MDH) but geometrically similiar. Vertical profile is assembled in the FMGS, based on the database coded waypoints and legs, and the AP/FD then follows it.
3) No. The vertical profile between the waypoints needs to be in the database too - this is the way how the machine recognizes the FAF. The FMS db coding standard provides both waypoints and legs inbetween them (path & terminator concept). The technology present on the flight deck only allows us to enter the waypoints, possibly with constraints, as you describe, but not legs. In turn, this is not enough for FINAL APP to arm or engage.
Nice explanation of path-terminators here, page 10 onwards:
http://www.icao.int/safety/pbn/Semin...202007/D.3.pdf