I live in an apartment with several fire sprinkler in the
ceiling.

CY: Good!

If the sprinkler goes off due to fire or malfunction, can I
turn it off
after the fire is out?

CY: No, the landlord or fire department does that.

Is it the same valve near the water heater or is
there a different one?

CY: Different one, which should be padlocked in the open
position.

I?Tm more worry about water damage (to electronics and
computers) than fire
damage. Perhaps because I?Tve never had a fire before and
this is the first
time I moved to a place with fire sprinklers.

CY: Time to talk to your local fire dept.

Alternately, is there a switch to cut off power to computers
or other
devices when it senses water? This would reduce
short-circuits caused by
water when the device is powered.

CY: Not sure.