Problem with water pressure

I recently bought a 2011 Rpod 177, and am having some trouble with the water system.
The previous owner had winterised it, and de-winterised it before delivering it.

I followed the directions in the manual to start the water system - fill the tank, open all the taps, start the pump - but I'm still not getting a good flow from the shower and the water seems aerated.
The gauge shows the water tank as full, and indeed it was filled to the top the the point of overflowing from the filler.
When the tank is full, the water to the shower is present but not an acceptable stream - it dribbles, basically.
When the tank drops below about 3/4 full, the pump won't shut off by itself, and the shower won't work though there is some water from the sink tap. I'm nervous about operating the water heater in case it is not properly flooded.

I note that the water intake fitting on the water tank is halfway up one side, rather than underneath. I was wondering if there's an intake hose actually inside the tank that is out of position and is sucking air, and if so what to do about it. E.g. is there an inspection hatch somewhere for the tank.

Check the winterizing valve. Near the pump there should be a valve connected to a short hose that goes nowhere. This is used to suck antifreeze into the pump during winterizing. If it was left open the pump will suck air. 

Just being sure: with the valve closed, you can't suck water from a bucket with that hose.

TT

Next thing to check is the debris filter right next to the pump. Unscrew the filter part and check for cracks.

Thanks for the suggestions, guys. I'm probably going to have to wait till I can tear the thing apart when I get it home.

I did find the debris filter, but that's upstream of the valve, so I'd assume I'd have a leak when pumping from a bucket, too. On the other hand, there's much less suction required for that so I might not have noticed.

The hot water tank, I'm pretty sure I did try most every combination - one tap open, both together etc.
I should check the seal around the anode; that was changed and may not have had new PTFE tape. But the amount of air I'm getting seems much more than a small leak would account for.

I was quite surprised at the wide flat water tank arrangement - my old camper had a deep narrow tank impervious to tilt. I did level the trailer carefully after I saw that but it didn't help.

I'm still wondering what exactly is inside the tank. I didn't have the tools to take it apart - at least, I didn't have a hose clamp to replace the crimp-on one if I removed that, or any tape/sealant to re-fit fittings.