You should look into getting a "whole house" filter system. These are fairly easy to install and maintain. the styles with the clear housing allow you to monitor soiling levels in the filter cartridge.
KMS has the correct solution for the water. But if your well is picking up mud such as this, you need to address that issue before you loose all your water. There is a filter on the well head that may be failing. When this happens more silt is drawn though the pump causing early wear and failure. That can be expensive. Much more then having a new well filter installed.
As far as the hot water heater. You need to put a garden hose on the hose bib near the bottom of the heater and while the water is still turned on run the hose until it comes out clear. A long hose going to outside placed in a bucket where you can see the dirty water running works really well. Once the water in the bucket become clear, you can turn off the hose bib and remove the garden hose. If the hose bib drips which happens all the time,. You can purchase for about one dollar a hose bib cap in which to screw onto the hose bib to stop the leak.
When flushing the hot water heater, if its gas, turn it down to pilot position so your not wasting gas trying to keep the water hot, and if its electrical or oil turn off the power until your done.
If you have never done the flush of your tank, I would not attempt it alone. Draining your water heater gas or electric takes some experience . You don't want to get burned or burn out and element on electric. I'd try to get help but make sure you flush your pipes and remove the aerators from the faucets and shower to get debris out of lines. There is much to know before you do this, it could cost you more doing it yourself
than getting a professional to do it. Just being cautious.