1
Refreshes are only kicked when there's a change on a server. Battery runtime - have no idea, but should not be a problem since you are connected to a big computer via USB = DR is being charged
2+3
There are two different USB realizations: passive USB and active USB. Only with the latter there's some current sent to the connection, so you can use other (passive) devices as e.g. wifi cards. There's a big guess that on DR devices the USB current is disabled
by design, thus DR itself is a passive device and cannot give life to other passive devices.
I've been considering using an active USB hub (with 4*AA batteries or a powerful 5V one

) which provides 0.5V to each connection. Then there's no problem in powering a standard wifi card + the whole installation is still portable. The last question is then compiling a wifi driver, but this does not look to be impossible.
Smth like
here.