Re: water pump not pulling water from fresh water tank
If the water heater is empty it will take a long time for the pump to fill it up before a full flow of water will reach the sink. Also, be sure all the low point drain line valves are closed. Of course if they are not you should have noticed some water under the trailer, but it's just a thought.
The most confusing part is if you are unable to draw water from a bucket, even after a prime, I would assume something is wrong with the pump. But that is only if you are certain you have the valve shut off to the fresh water tank and then the valve is open to the suction side of the hose to the bucket. Some time the off or on for the valve can get confusing, but generally on is when the valve is in line or the lever turned in the same direction as the hose it's connected to.
This may not be any help at all, but I'm just throwing things out, just in case there's been something overlooked.