OK, since nobody else has responded, I'll chime in with a few thoughts.
First, congratulations on the new home. The room looks big enough for a good setup. There are alot of questions here, so I'll take them one at a time. Bear in mind, this is just my opinion, keeping your 2 to 3K budget in mind.
1. That window is an issue and personally, I would address it with some blackout curtain or blinds. If you plan on watching anything on a project in there during daylight hours I think you'll find that its going to impact the image. You can still put your screen in front if you like. A portable manual pull down or a wall-mounted drop-down screen would probably work, but you will need to do something with that window (especially that top bit).
2. Lots of screen options. Pull-down screens, while convenient can develop wrinkles over time unless you get a tab-tensioned screen. So I suggest if you are going that route you should be looking at tab-tensioned if your budget will allow it. I personally prefer a fixed frame screen on the wall as it will give me a perfectly flat surface and that inst going to develop any creases or wrinkles and there are plenty of options to fit every budget. If this were my room I'd probably be doing blackout curtains or blinds on the window and looking at one other the other walls for a projections screen Without any measurements, it seems like you have enough room for a screen on the wall with the entertainment unit, depending on how big of a screen you were thinking of. If you've got 7' there, I think you can make it work for maybe 100" or 110" screen. If you want to go bigger, you may need to project in the other direction.
3. I don't see any closets so I am assuming they are on one the other walls. Shelf mounting can work but it will impact your projector selection. First there is the question of whether you are sitting your projector on the shelf or hanging it under the shelf inverted. Keep in mind that the W1070 you mention as one of your possible projectors will project its image with the bottom of the projected image basically equal to the bottom of the screen (there is a small offset but you get the picture), so in order to fill up your screen the project is either set at an elevation equal to the bottom of the screen (not practical for shelf mounting at the rear of the room) or the top of the screen (in which case you need to invert the projector and hang it from the shelf. Second, if you are shelf mounting I'm guessing your throw distance will be about 20'. You'll need to look at the calculators over on projector central. The W1070 isn't really a good choice for a 20' throw. The Optoma is a better choice for this distance, but realize that at 20' you will be getting a very large image - something around 160" diagonal. I'm not sure if that the image size you were thinking of. Its a bit on the large size, so that's probably something you want to think about. I suggest you get over on projector central and go through the list of top 10 home theater projectors and play with the calculators. You should think about how big you want your screen, and based on that, where you will need to put your projector. I think you may find that you will need to think about a ceiling mount.
4. If you put your gear in the closet, you can control it all with IR blasters. You may need to do something special with the PS4 - i believe that's Bluetooth. but there are adapters to make it work.
5. Yes, you will want an AV receiver. They will not negatively impact quality. As for lag, there may be very slight hit to input lag but nothing noticeable. A little more research may be needed here, but I game online all the time and have never noticed any perceptible impact from going through a receiver. Once of the reasons I went with the w1070 was due to its very low input lag numbers.
6. I suggest you go over to projector central and look through their top 10 home theater or home video projects. They are all popular choices. Optoma is a well-respected name in projectors so there's no worry there. There are a lot of good projects in the $1200 and under range and I think thats where you should be looking to stay on budget. That said, the W1070 seems to be the best of that price range.
7. You might as this question in the audio section and give them your budget up front, but some general advice here would be to avoid a home theatre in a box. Get a receiver and a 5.1 speaker system. The guys over at Audioholics have some recommendations for a $1000 system. http://www.audioholics.com/recommend...mmended-system
. This is more important than you think it is.
8. So for a sample system lets start with something like this and adjust it from there:
Projector - BenQ W1070 = $900
Screen - either fixed frame or electric = $600 - you should be able to find a screen from Elite or similar in this range depending upon final screen size selection.
Cables, mount, etc - Monoprice.com = $200
Electrician to get power where you need it = $300
Audio system above = $1000
Total = $3,000
9. I am a fan of couches and chairs versus home theatre seating but its really a matter of personal opinion. You can blow your entire budget on either one.
10. If the white ceiling gives you problems with reflection, you could consider painting it a darker shade or a flatter finish (eggshell, etc). My other big recommendation is a popcorn machine.
11. sorry - no suggestion here. I use a PS3 for 3D bluray. There are a ton of good players out there. Quick Google search should turn up a raft of reviews.
Hope that helps