Why does rear tire lose 35 psi in a week with new innertube and tire?
A possible (even likely) cause is a leaking valve. The simplest thing to do first is to see if blowing air out if the valve (by depressing the pin) solves the problem. You wouldn't see the dust if it was there; the only way to know is to inflate the tire and wait a few days.

If that doesn't solve it, or you are less patient than that, go straight to the next step: remove the tire and tube. 

When removing the tire, use some chalk or some other means of knowing how it was mounted on the wheel (regarding the valve position and which is the drive side). With the tube, also take notice of which way around it is on the wheel. Now, if you find a hole in the tube you know where to look for the cause in the tire.

Remove the tube and check for the leak by immersing the entire tube in a tub of water.

Be patient, because the leak is slow.

You could have pinched the tube when replacing it (common, but usually leaks faster). But more likely, you still have some glass in the tire. Line the tube up with the tire and check carefully. Patch the tube.

But I really suspect the valve. From my limited experience with Schrader valves they a more prone to leak, especially if used without valve caps.

Other possible causes are a foreign body onside the tire or something (eg a spoke) protruding from the rim.