Please look at my drawing and comment if I am doing this correctly. I am in Pennsylvania and our building codes are the Uniform Construction Codes which basically refer us to the 2009 International Codes issued by ICC. So I have read over the international plumbing code and in particular Chapter 3 & 7 which deals with most of what I am looking at here.

I want to add a bathroom (WC & Lav + 1 additional remote sink) in a heated pole barn which has a 6" slab on grade floor.

The picture is a top view only.

At the bottom of each stack and the WC I was going to use 90 deg drain elbows to go from vertical to the horizontal lines in the pictures. I was planning to wet vent the WC using the drain/vent stack that the bathroom sink will connect to and then proceed out the roof. The remote sink in the middle of the barn was going to connect to its own drain vent stack and continue out the roof.
All drain lines will slope at 1/4" per foot toward the septic.

Does anyone see anything wrong at this point?

Couple of additional questions...
1. Since the floor has not been poured yet I have about 10-12" from the top of the concrete to the undisturbed earth. Do I need to set these pipes in a trench filled with sand? Total horizontal distance is about 30 ft to side wall so I need a drop of 7.5". Or can I use the gravel we are putting down under the concrete to support the piping?

2. The code mentions freezing but section 305.6.1 Sewer depth does not give any measurements...is that because there aren't any?

Thanks