First of all call a pool company! Are you sure that you don't have a "mustard" algae problem? The heater needs to be looked at and the only way to get rid of rust particles is to vac to waste. You need to address the real problem because you don't want to swim in the pool the way it is. A pool company will test your water at a minimal cost and advise you for free.
Rust deposits from your heater are possible if your heat exchanger is old and has glass lined headers. The glass installed by the manufacturer is starting to deteriorate and it is exposing the steel underneath. The rust swells and then breaks off.
no you need a stronger heater specifically designed for a swimming pool
You can buy a swimming pool heater in the Burlington, Vermont are at Leslie's Pool Supplies. They have a great selection.
Unless you leave the heater on, Yes
Hot water is often cloudy due to the presence of dissolved air that is trying to come out of solution - the air dissolved in the water when it was cooler and when the water was heated up the solubility of the air decreases.
There are no combination heater/cooler units that we are aware of. The would have to be separate units.
That would depend on which heater model.
To stop the black residue from a baseboard heater, the wall around and near the heater should be cleaned as there are dust particles attached to the wall. This is called ghosting which fine particles of soot attach to the wall that is cooler than the temperature.
Cloudy water indicates you have air mixed with the water. It is common for hot water to be cloudy when you first turn on the faucet. It should become clear in a few seconds. The air in the water will do no harm. If you have a well then there may be a problem with the well. Have it looked into by a professional.
I'm guessing that you have build up in your water heater, just drain it and you should be fine.
Try a pool shop
it warms the air particles... witch then transfer the heat to you
Copper, check your tablets or algaecides or maybe you have a heater.