It is unlikely that copper piping is your problem.
It sounds as if the restriction is either 1.)in the valve that supplies the cold water to the heater,replace valve or 2.) In the pipe just as it leaves the water heater (some heaters have a small ball that acts as a heat trap) it may be stuck in the pipe. Remove pipe as it leaves water heater and inspect.
Since all of your fixtures act the same with low HOT water pressure, it is doubtfull that the problem lies with each fixture.
It has to be one of the above.
The Local Plumber
Tustin, California http://www.TheLocalPlumber.com