Lets say player A plays a unit. Player B attacks it but is killed. Is it player A or B who should play next?

thanks!

Yes. You take it in turns to play cards, either onto existing fronts or creating new ones. If one player runs out of cards the other player can play their hand.

Calevan said:

Player A should play next, since "alternating back and forth, each player must play a unit from their battle force.........until both players have played all of the units in their battle forces." (rulebook, page 24)

thanks for the help!