I'll try and answer...
FLEX - the derate used for takeoff. If full power is not reqd for takeoff, the performance books (usually airline specific) will reveal the FLEX temperature to use e.g. +48C.
A. It is then entered into the FMGS Perf Takeoff Page.
B. Then on takeoff, you set the TLs to FLEX (rather than TOGA), and the reduced power is set.
If you do B without A it writes a rude message on the screen, and suggests you apply Full Power (TOGA).
<<Is the free movement for non-autopilot landings >>
1. Be aware of non-autopilot v non-autothrust. The systems can be enabled / disabled largely independantly.
2. Between Idle and Climb (or Flex/MCT with only 1 engine) the TLs work as any other aircraft with AT disabled. TOGA is essentially a "switch position" asking for full power.
NoD
On an A320 course!