I was wondering whats the max height when a GPS lets say this one...
...doesn't send information.
You mean like when sending a rocket or something up?
As long as the temperature doesn't go below the GPS units functional range, this will not be a problem you'll meet, as the satellites orbit at around 20,200 km and the signals will be available at the same distance on the "other side", so as long as your rocket doesn't go more than 40 thousand km out, the signals should be fine.
And does a GPS actually send or just stores information?
Neither, if you by send means "transmit wireless".
It communicates on a couple of wires and you do the rest - storing or transmitting.
You really need to read the manual!
If not how can i send it to a server/computer?
Like any other signal that you want to transfer.
Without knowing your application, it's hard to be precise.