!!!!!Need Help/Advise With Theater Setup!!!!!

I am in the processes of getting my basement renovated.I am thinking of this setup below.
This is my first time doing anything like this and I have done some research and thought would ask you guys for some help and advice.

My main problem is my ceiling in the basement is only 6'10" and I have the support columns as you can see in the image. I have 10' from the side wall to the column and I would like to put a 100" screen if possible.

My Viewing distance is 15'-20'. I wanted to know how do I ensure that i get 100" Diagonal image?
At what distance do i have to mount the projector to make sure the image is contained exactly white part of the screen or can i just change it in the projector settings and if so will that will hurt image quality?

I have looked at the various calculators and cant figure out if it will work out with the low ceiling or not. Any advice help would be greatly appreciated Thanks

Equipment List:

1.Epson PowerLite Home Cinema 8350 - Epson
2.Elite Screens R100WH1 ezFrame Fixed Projection Screen (100" 16:9 AR)(CineWhite)
3.White Precision Gear Universal Projector Mount (PRG-UNV-W) - Peerless
4.Pioneer VSX-1021-K 7.1 Home Theater Receiver
5.Fluance SX Series 7.0 Cinema Surround Sound Home Theater Speaker System
6.Fluance DB200 12 Inch 200 Watt Low Frequency Powered Subwoofer
7. Logitech Harmony 900
8.Mediabridge Ultra Series - High Speed HDMI Cable With Ethernet - (3 Feet)
9.Mediabridge Ultra Series - High Speed HDMI Cable With Ethernet - (25 Feet)

Thanks for your response BIG. So if i mount the projector at 15' I should be able to get that image and if it smaller or bigger then the screen that I purchased I should be able to change it in the setting of the projector without losing image quality? Basically i don't want it be like once I have mounted the projector on the ceiling the image is hitting the ceiling or the floor and there is nothing i can do about it.

You also suggested to move the furniture closer my whole reason for having the sectional 15ft away was because the bottom of the screen is only 1.4ft away from the floor and i might be too close. The ceiling which is 6'10" Total of 82" Width of the wall is 10' Total of 120"

The screen frame size Width is 91.7" - Height 53.5"

So my screens frame is be only 1'4 above the floor and ceiling If i deceived to mount in right in the middle on wall Is that ok?