J P F
Let's say Parman (Rapid Assault 2) activates in the combat phase and uses his rapid assault ability to move into another friendly grid that has not yet activated. Do the units in Parmans new grid receive the rapid assault buff?
Yep. Per the explanation of Buffs on p.13:
A unit with a buff, and any units in the same grid as that unit, always have that buff.
So a unit with a buff always has that buff and the ability to confer it on other units in its grid. And per the Round Summary on p.33, Combat Phase (II) and Movement Phase (II), each grid is checked for buffs as soon as it's activated, so as long as there is a unit with a buff in the grid, that buff is conferred to the other units in the grid. There's nothing in the rules to indicate that a buff is "expended" for the turn when a unit with a buff moves or is otherwise activated.
Mines. Do these get removed once a unit has moved into them and suffered an attack roll?
Nope. There's nothing in the rules to suggest this is the case. Of course, if you feel minefields are OP, there are always house rules...