1) When you explore new horizons and you have the maximum areas in play you are not allowed to remove any one area that has a trap, encounter or a party in it, does this also mean that if your party is in the area you are also not allowed to remove it?

2) When do you play advantage cards during combat? The way I see it combat rolls out like this:

1- Calculate combat rating for both parties. Check Monster/character passive habilities

2- Use character skills, play advantage cards.

3- Roll Dice.

But are you able to use an advantage card that adds combat rating after the dice result?

1) No. You bring in a new area, place an encounter on it, then move to it, then discard an area from play (if you are over the maximum and are able to). So your party is always in the newly added area when you discard areas.

The rules also say that players declare whether they are leaving their current area during the reset phase. It's not completely clear, but I think they intend for everyone who is going to travel this turn to leave the areas they were in last turn before the movement phase. (If you are playing the 1st edition, you may want to look at the revised edition rules on the anima support page. I don't have 1st edition rules here, but I think that the seeking new horizons rules changed a bit)

2) If the card type is 'Combat', then it can only be played in step 2.

If the card type is 'Interruption', it can be used at any time, including after rolling the die in step 3.

Character abilities can be used at any time (including after the die roll), unless they say otherwise in the description. (I think the only cases of restrictions are abilities used in the reset phase or the movement phase.)