(1) Let's say the active enemy has a war column of strength 3, their topmost instruction is peace 4 and they have plenty of action points available. First they execute the peace instruction which ends the war and moves over to the inactive column. The war instruction underneath the war column then returns to the topmost available space of the enemy instruction display, which is the space just freed up by the peace instruction. the war instruction that has just been removed is the next instruction to be executed.
No. An Enemy Instruction counter moves to the Inactive column only after the Instruction has been fully executed. Re-read Rule 6.3.5, step 2, first bullet.
(2) During a take actions operation, after activating all bands in a rancheria, the player make activate the same band again and again and again until they run out of action points
Yes (Rule 4.1, step 4); just don't overlook the cost: it's as many APs as the Band's strength, not just one AP per re-activation.
(3) If a development card forces a 1 round battle the player doesn't lose the unit involved even if they lose the battle. They just lose military points.
If you mean Cards #66 and #72, then the answer is yes; see the FAQs.
(4) Once Medicine Lodge Treaty is in play only 2 development cards are discarded and drawn during passage of time because MLT takes up one of the development card slots for the rest of the game.
Yes, that's the meaning of "This card may never be removed from play".