a) When a Mythos card is drawn and it says a gate opens at the black cave and there is already a gate there do monsters appear at all gates? If so, does this include gates that investigators have already entered and are now in the other world?
Per the FAQ, this is a monster surge, and the number of monsters that appear is equal to the number of open gates or the number of players, whichever is greater. These monsters are evenly distributed across all open gates.
b) When an environmental card is drawn i know they stay in play until new environmental cards are drawn; but i was wondering about monster movement phases; does this mean that the monsters that match up with the symbols on an environmental card that has been in play (it has already been drawn and the monsters have already moved for that card) for awhile still get to move according to those symbols AND also the ones on newly drawn mythos cards that are not environmental? Or is it once monsters have already moved for that particular environmental card that environmental card no longer applys to monster movement?
Once played to the table, ignore the movement symbols on the environment card.