Fresh water tank leaks can be repaired with some patching material obtained at an RV place. If the leaks are on the bottom, it can be repaired without removing the tank. It connected to a waterhose from my house which is on city water.
Your faucet and toilet leaks are probably from non-use and may go away on their own as everything is re-hydrated.
The hot water valve stem may now be clogged on your faucet. R&R. You may want to put a filter on the line going into your water pump like this one:
http://www.amazon.com/SHURFLO-255-313-Twist-On-Pipe-Strainer/dp/B000V2W0GE
and use one of these on the water hose you use to fill the tank:
http://www.amazon.com/Camco-40043-TastePURE-Flexible-Protector/dp/B0006IX87S
I hope you are using a white or a blue RV water hose as a regular garden hose is not for potable water.
You also want to get a water pressure regulator if you are connecting to city water:
http://www.amazon.com/Camco-40053-Brass-Pressure-Regulator/dp/B000BQ7WH2
If you have not removed the anode rod from the hot water heater, this would be a good time to do it. Release any pressure in the system before removing this replaceable anode rod as 6 gallons of water will come out. Spray out the HW tank to remove the calcium. There is a special "wand" that goes on the end of a garden hose for this to spray the back part of the tank to wash the calcium out the anode rod hole. This is twice a year maintenance. If the anode rod is down to just the smaller than a pencil metal rod, replace it asap as your tank could start corroding away (leak). The anode rod is the sacrificial metal to stop the tank from corroding.
My drains for the shower and the sink have the same twist in stopper. Counterclockwise to remove and drain. If this is not the problem???? There is not a valve other than the drain seal in the tub that I am aware of.