Computers and telemetry all need electrical power, is this just stored in batteries? If so what type of batteries are used? How much electrical power does a modern rocket consume on normal LEO or GTO flight?
For rockets it's normally batteries since they only need to operate for minutes, maybe hours at most when it comes to upper stages.
An example power budget and description of the hardware for one of the largest launch vehicles out there, the Ariane 5, can be found here. It's a bit outdated (2002) but you can get a feel for the numbers. Ariane 5 used to deliver 4 kWh over 6 hours with peak power consumption of 1100 W. It used Ag-Zn batteries, but lithium-ion are now getting increasingly more popular in Space so the newer launchers probably use those.
This'll, of course, scale with the size of the launcher.
Batteries usually. They're charged on the ground and discharged during flight.
Sometimes fuel cells are also used, although that's more typical for manned spacecraft such as Apollo and the Shuttle.
And in the case of the Shuttle the orbiters also required hydraulic power to actuate their flight surfaces, provided by hydrazine fueled auxiliary power units (APUs).
As an aside, many military rockets (such as shoulder launched guided missiles) use thermal batteries which are capable of remaining "charged" for decades while not in use. Such batteries use a solid electrolyte which renders the battery inert at ordinary temperatures. A small pyro charge melts the electrolyte, activating the battery and enabling it to provide power.