Is there insulation in the ceiling of the garage ? If there isn't then whatever temperature it is in your garage that will be the temp of the floors in the living space above and that will make the insulation on the doors that much more important. How cold/hot does it get where you are ?

Does it need to be evenly distributed ? For heat/cooling retention to be even across the entire door, yes. If you don't care if some parts of the door are less well insulated than others then no.

If your only concern is removing weight from the door then yes, you can remove some/all of the insulation but you need to keep it distributed so that there isn't a lot of difference in the weight of one side of the door vs the other (vertical does not matter as much as horizontal as you don't want one side of the door lagging behind/ahead when the door is being opened/closed).