Not a big deal, though typically something like solvent or avgas works better for cleaning an engine because water won't do jack to the oil and grease on it. The rough mag thing is unrelated, if you have a bad mag drop/rough engine on a fuel injected 172 it's probably a fouled plug from taxiing too rich. Those things are known for that, even when properly set up
Exactly. Back when I used to get to wrench on airplanes, our shop had a pneumatic spray gun that ran on compressed air and siphoned mineral spirits out of a drum on the floor and we'd hose down the engine with it. Works great, but leaves a giant puddle of dirty solvent behind. Definitely something you have to do on a flat shop floor and not on a slope or over a storm drain.
As for throwing cold water on a hot engine, I would only worry about the possibility of thermal shock. We always hear about "shock cooling" when it comes to making quick power adjustments, but I would be way more worried about pouring cold water on the block! I wouldn't be too worried about water getting into the fuel system, because unless all the fuel lines and injectors are water-tight, you'd get fuel leaks anyway! Fuel + hot engine = Fire. Fire bad...
Spark plug fouling, especially on the bottom plugs, is the culprit. If it's only a little bit fouled you can taxi out to the runup area, throttle all the way up to 2000 RPM (or more), and gradually lean the mixture WAY out. Run it for a minute or so and watch for your peak RPM to increase and listen/feel for the engine to smooth out. The point is to lean the mixture enough so that you're burning all the unburnt fuel out of the inside of the plugs (perhaps softening and taking some of the lead fouling with it) rather than adding it (which you do when running the engine full rich while taxiing). Throttle back to 1000 RPM, mixture Rich, throttle 1800 RPM and re-check the mags. This procedure works great for small amounts of fouling that are "burn off-able," but if enough people have had the airplane before you and sufficiently fouled the plugs, sometimes the only way to get it all out (especially the lead fouling) is to have an A&P remove and sandblast the plugs.
I would be weary of that procedure on larger high performance engines, which require specific ROP/LOP temperatures, but the small block non-high performance Lycomings found on C152/C172s are pretty bulletproof. Please feel free to correct the above since it's been a while since I've had to do it.