We use a stove-top percolator. They are light weight, inexpensive, and very durable. Buy a stainless steel one, and forget the REALLY cheap aluminum ones.
Water filtration depends. As others have suggested, you can always fill your fresh water tank (after sanitizing it properly) and drink that water. A Brita pitcher is also a good idea. But one essential you've not mentioned is a water pressure regulator, and not one of the cheap $10 ones, but a high quality one (probably $50-$80). You won't need it but rarely, but when you do need it, it will be absolutely critical. Your rig's plumbing can probably only take 80 psi, and I have been in two campgrounds where the supplied pressure was 150 psi, which will explode your plumbing. VERY expensive to repair.
Screen rooms, others have addressed well.
The same things you found crucial tent camping will serve you well in the new camper. Welcome to the scrum, and may that camper bring many joyous years of camping delight and lots of fabulous memories.