bathroomplumbingshower
Similar to how you can control the flow of water between a tub faucet and a shower head, I'd like my new shower to control water between a rain-head shower from the ceiling and a handheld shower on the wall.
Can I buy a shower kit that contains a shower head, temperature valve, and tub faucet, and just use it differently somehow? Or is there a better way?
Diverting the leak up to the shower head using the diverter valve should not be a problem, but your assumption that fixing it will be "pretty easy" may not prove to be true. You are correct in that hot and cold supply to the tub/shower valve needs to be shut off. Sometimes apartment shower valves have built in shut-off valves called integral stops.
Sometimes apartments are equipped with individual remote shut-offs. Sometimes the whole building will need to be shut down. Removing the valves may require special tools like deep valve sockets.
The repair may be simple washer replacement or may require more complicated cartridge replacement.
I do recommend that you try it but make sure your landlord is cool with it in case something breaks, and have back up shower facilities available in case it ends up being out of service for a while.
Hardly any noticeable difference; though a "high flow" showerhead would make any difference WORSE, not better, as well as increasing your water use needlessly.
The water is already traveling through many feet of pipe to get to the bathroom. Whether there's 4 more feet of pipe to the showerhead or 9 more feet of pipe to the showerhead makes very little difference, particularly at the typical 2.5 GPM flow. At a more efficient 1.5 GPM flow, even less.
4 feet of 1/2" plastic pipe @2.5 gpm = 0.625 feet added head. (0.27 PSI)
9 feet of 1/2" plastic pipe @2.5 gpm = 1.406 feet added head. (0.61 PSI)
4 feet of 1/2" plastic pipe @1.5 gpm = 0.243 feet added head. (0.11 PSI)
9 feet of 1/2" plastic pipe @1.5 gpm = 0.547 feet added head. (0.23 PSI)
There's also no particular reason to put the valve set closer to the spout - so you could just put the longer pipe on the spout, and take advantage of the pipes in the shower wall.
Best Answer
What you want is called a "Diverter Valve". That will give you something to search for, because you will find all different types depending on they style you want and how many shower heads it needs to handle. And example can be seen here:
http://www.signaturehardware.com/three-way-in-wall-shower-diverter-lever-handle.html