Kemet: Blood and Sand

You may use both kinds of move during a Move action, but if you teleport a Troop its Movement value is not used and a Troop can never teleport more than once during the same Move action; teleportation costs 2 PP and moves a Troop from a District with a Pyramid to a space with an Obelisk (p. 8).

Yes — recruiting into a District controlled by an opponent immediately triggers a Battle in which you are the attacker; if you recruit into multiple enemy Districts you choose the order to resolve those Battles (p. 7).

To buy a Power tile you must control a Pyramid of the same color that is at least the same level as the Power tile (or use the alternate buy option for an opponent's City), pay PP equal to the tile’s level, and you cannot buy a Power tile whose artwork you already own (p. 7).

Only the attacker and defender are involved in a Battle; during the War Council each may hide DI cards with the Battle icon under their in-hand Battle card (this is the only time DI cards may be played for that Battle), and no other players may play DI cards in that Battle (p. 9).

First each player loses Units equal to the opponent’s total Unblockable damage, then each loses Units equal to the opponent’s Damage minus their own Defense; note Strength (and thus the winner) is determined before casualties and the winner still counts even if they subsequently lose their Troop (p. 9).

At the end of the Day Phase each player must have at least one Action token on each of the three levels of the Pyramid on their Individual board (p. 6).