1. Correct, just rinse in water.
2. T shape is control valve as you guessed. Doesn't matter which way you flip it.
3. The check valve IS directional! If there is no arrow showing air flow direction, blow into both sides. The "easy" side goes towards the pump.
4. Order of install is important. Control valve goes after pump (say 6" away), then check valve as close to the water level as possible being a nuisance. This was if the pump goes off, it will siphon minimal water if any at all.