That's a lot of lumens for a small image, but should be bright and vibrant.
My biggest concern is the projector placement. You must download the owner's manual and ensure that placing the projector in the orientation you are after is feasible with that unit.
You must always allow manufacture recommended, or more, airflow. So, no setting the projector down in any way that covers vents.
For rear projection, a covered area in the back that doesn't let light in will drastically improve image quality - this area must allow enough airflow around the projector to leave a quality image.
Your idea sounds interesting, but some homework and digging will be necessary to ensure it all is allowed.
I'll do it on this one...
At the bottom.
"In upward and downward projection..."
YUP! You can do this, so that's great news.
May be tough to keep that mirror as small as you want, but you have to have the space to get the size you are after and total lens to screen distance will remain around 5' or so.