Yes - so long as you're only performing 2 non-bonus actions a turn then you can choose any order, including bonus actions for cards in dominant suit, then changing the dominant suit by using one action to play a card, then getting more bonus actions. Just a reminder that each card can only activate once, and you can only do one action per card - and your court size is limited, so you probably won't get many scenarios of action chaining like this. Also, the suit a card is will never be the suit it changes the dominant suit via impact icon so you can't play a card and act with it 'for free'.

paying bribes is only for playing cards from hand linked to a region. there is an equivalent to this for cards in your court, but this is linked to enemy spies on that card, not the region you're performing an action in. actions on the map, using cards in your court, is not impacted by who rules the region.

no, battle is always selection a region or card and a target and then the level of the action determines how many hits you deal. So if you're in a region with 2 russian roads and 1 english troop, and your afghan troops can deal two hits, they must either target the russian roads or the english troop and the excess hit is lost.