Fairly typical problem. Definately try the easy stuff first... clamps, screens, etc. Oh and make sure your one of your tanks isnt empty. On my boat, I have two spigots that control the port and starboard tanks. If they are both open and one emptys, bingo! A water spitter.
One fairly common symptom of an air leak, assuming you have pressurized water and not a foot pump is... well first I would recommend pouring yourself a good boat drink. Then locate your system pump. Now bleed the air out of the lines, turn everything off and sit down. If you have a leak, your pump should cycle on and off for just a second or two because it is trying to maintain pressure. You should hear it.
If that doesnt happen, then the leak may be upstream of the pump, specifically between the tank feed and the pump. Also if you can get a visual on the pump, turn on your water and make sure the diaphram on the pump isnt leaking.
The hot water, hmmmm. Any work done lately? Hooked up backwards? Check valve possibly. Good news is a replacement is barely a quarter to a half of a boat buck.
Good luck