1. I had this on my brand-new TM. Turns out the drain in the kitchen sink was a little leaky, and wouldn't sit flat on the sink. I unscrewed the drain and reseated it using a little plumber's putty, screwed it back in and no leaks/water since. You may also want to check to make sure the vent/overflow tube is connected to the outside properly; mine isn't (for now), so that's a source of water on the tank as well, if you overfill the tank.
2. City water -- you should be using a pressure regulator when you hook up a hose to this outlet. The rule of thumb I've always heard is no more than 45 PSI should be going into that port, and there's a one-way valve right behind that port. So, if you're coming in with a lot of pressure, it's possible that you're getting some back-pressure and that's the cause of the leaking around the hose. Conversely, if the one-way valve is somehow blocked, then you'd get no (or very little) flow into the TM at all, just leaking around the hose connector.
3. I'm not getting a good picture of where the leak is coming from, so I can't hazard a guess until I get a little more info
4. Sounds about right. That's what mine does, at least.