Can't help with a lot of those problems...
The winterizing kit, though is probably just installed backwards. As RoadRunner found on his... The winterizing valve is a diverter type valve. In it's correct fitment, the valve connects the pump to the freshwater tank, allowing freshwater to flow through the system. In the "diverted" poistion it connects the pump to the antifreeze siphon pipe allowing the pump to draw from the antifreeze bottle. You'll notice the operative phrase "connects the pump to..."
If it is installed backwards it then becomes; it connects the freshwater tank to the pump...that still allows water to flow from the tank to the pump and you won't notice anything wrong. However, when you go to winterize and turn the diverter handle, it connects the freshwater tank to the antifreeze siphon hose
and the pump can't draw anything; not antifreeze or freshwater.
The remedy? Take the valve out, turn it 180 degrees and put it back in. A bother, for sure, but, easily corrected. The little valves are marked for "pump side" or "flow direction", but, in the haste of installation, it is easily overlooked and it isn't something that is readily "QC'd" at the factory as the valve, installed correctly or backwards, will always connect the pump and the freshwater tank. It is only upon winterization that it becomes apparent that it is installed backwards.
Need a little more information on the antenna problem... Is the amplifier light "ON", will it come "ON" at all? You checked all the connections, even the ones to the wall plate? If you go up on the roof and pull the connection from the antenna head, using a VOM, do you get 12v across the connector? There should be a 12v fuse in the fuse panel for the TV, is it good? Unfortunately, there are a lot of places for the signal path to go wrong. Could even be the amplifier in the atenna head has gone south (if it has, I recommend replacing it with a Jack Off The Air Antenna; one of the first "mods" I do on a new trailer, even if I'm not having a problem).
The black tank rinser is probably something as simple as the backflow preventer valve is broken. They aren't too terribly "rugged" (the ones that the manufacturers use; read "cheap") and they can self-destruct leaving the hose blocked in both directions instead of just one...
Yes, there are an awful lot of "quality" issues with today's RVs, but, on the whole, for what RVers are willing to pay for a rolling house, completely furnished and with all appliances furnished, it is to be expected. It amazes me, sometimes, that we are willing to pay north of $30,000 for a car, but, complain mightily when we have to pay $18,000 for a rolling house with all the amenities. The companies have no recourse but to cut costs and the only places they can cut costs is the quality of the included parts and the quality of assembly. We've basically got no one to blame but ourselves. On the whole, for what we "pay", I think most of us get a pretty good deal for the dollars invested; minor problems are to be expected. Some of us get what appears to be "more than our share", but, we all have them, it is how we deal with them that makes the difference. Take a deep breath, realize it isn't personal, get them fixed and enjoy your traveling house. And remember, just like your sticks and bricks; what isn't broken today could well be broken tomorrow, it is part of the price of admission.