1) tuning is a process done where they look at fuel and timing maps to maximize your engine's efficiency and power. Each motor is different and depending on setup these variables change. The tuner will hook up a wideband o2 sensor and run your car on a dyno to see what the air fuel ratios are and adjust fuel and timing to avoid going lean (too little fuel) and too rich (too much fuel). There's more involved but I'll keep it short. The tuner will also use an ECU to program this, giving you a 'tune' or map that he will later load into your socketed ECU (if using Crome etc) or it will input the data onto Hondata's ECU.
2) The best ECU for your setup if you're getting a tune will be a p28... I know someone will bring up other good choices, but usually tuners use a p28 or other socketable/convertable ECU.
3) I can't answer about the fastest possible, as that all depends on how much you're going to spend and on which parts.