I have not connected the auxilary network cable from the back of the AirPort Express to the XBox unit yet. I would not think that should make a difference but that is the only difference between now and how I had it set up before when I was experiencing issues.
The Xbox may have been hogging the available bandwidth on your network, which would not allow additional devices to connect to the network. Unfortunately, Apple routers have no settings to control the amount of bandwith that is allocated to each device.
If you hook up the Xbox and find that some devices will now not connect to the network, that would explain the issue that you first reported.
Timed Access is whole other discussion, so you'll need to start another post if you are curious about that.
As far as screenshots are concerned.....
Hold down command-shift-4
position the cursor at the upper left of the area that you want to capture
Click and drag diagonally down to the right
When you release the button on the mouse, the shot is taken
My shots appear as a PDF file on desktop
To insert a screenshot in a post, click the camera icon and navigate to the location where the PDF is located, select it and click Choose, then click Insert