moving electric water heater to old shower cove
You can move the water heater to just about anywhere that would be convenient. However, it is not a good idea to reduce the size down from 3/4" to 1/2" directly off of the tank. You will likely run into issues with water pressure.

In branch plumbing, it is best to keep the size of the pipe at its maximum until it branches off to a specific fixture. Most fixtures, with the exception of a toilet takes 1/2". A toilet is actually reduced to 5/8" by the time it gets to the fill valve. 5/8" is an odd size in plumbing, so most plumbers typically run 1/2" anyway.

You should try to extend the 3/4" pipe as far as you can go, and then tee off of it using multiple 3/4 x 3/4 x 1/2 tees. When you tee off, try to make that run directly to a fixture without teeing off again. This will greatly help keep the water pressure balanced. If all of the plumbing is 1/2", then the fixtures will compete against each other for water because there is not enough volume of water coming through the pipe.