Yes. You can reliably see ISS in urban locations -- it's actually quite cool to do a few times.

It will be a point of light, moving very fast against the background, just as shown in some of the animations in OP. If the geometry is set up so you can see the whole overpass (nearly horizon-to-horizon) it will still last only a couple of minutes.

It will happen around sunset, when the sunlight is shining on ISS, but it's dark (or dusky at least) on the ground. You don't see ISS easily at night because it will be in Earth's shadow.

Yes! As long as you can see a few stars then you should be able to see most of the satellites that the site shows. The International Space Station in particular can be brighter than any star.

The Moon and ISS are pretty easy to see almost everywhere.

Yes, I've seen many satellites from the city. I even caught a iridium flare randomly one night. A good time is about 1/2 hour after sunset.

Yes for the ISS. It's the brightest satellite most of the time because it's huge compared to the rest.