There are 2 reasons for the t-molding in the closets. The first one is just to make it easier on you. Your Pergo is longer than the door is wide, You can use 2 pieces to get it under the jambs or make it easy and rip it to fit under the jambs and put the t-molding. The second reason is all of the laminate will be held to gather by a 2 foot join going in to the closets, you will get enough movement out of the laminate that that join will come loose over time. If you have T-molding there each side can move independently of each other and you will never have to worry about it.
As far as putting quarter round against the base I probably would, you are covering a large area and you will get a fair amount of movement out of the floor, 1/16 of an inch does not allow for much movement with out coming out from under the base. You could go with a 1/4 inch expansion around everything but in my experience for an area that large I prefer a wider expansion joint. There is less chance you will get binding from the movement of the floor. If you live in a humid area I have seen the laminate expand and shrink by around a 16th of an inch per plank so I prefer to leave a larger expansion joint around the perimeter.
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