A:Answer The answer to your first question is: It depends. The strength of the signal from the router, as well as how many "obstacles" are between the computer and the router are going to make a big difference
The computer should not overheat while in the bag. Sleep mode draws very little power. However, if you wanted to do a quick test just to verify it, you could put the computer into sleep mode and then put it in the bag for an hour or so.
Finally, it does have Bluetooth, so you'll be able to connect other Bluetooth devices to it.