Not to say that high poly counts can't drag a game to a halt... but I've heard more and more that poly counts (unless over the top) don't matter. It often comes down to texture stress, size, and other stuff. But I'm no expert...

Anyway, here's my short anwser:

I would attempt to keep anything below 5,000 polys. (And the smaller amount the better - more doesn't mean more detail.)

1. How much polygons must an object have to be considered "high poly"?

just one more than needed...

but that depends on the object you want to model... there's no specific polycount for any object, just use the less polys as possible

For a complete character, I would not use more than 3.000 polys, including weapons and all stuff...
My cars are around 2.000 polys...
For a level I would recommend to have less than 20.000 polys, including vegetation...
For props, have an average of 100-200 polys, maybe less... a cell phone can be done with just 6 faces

As stated before, the lower you can go the better. it all depends on the engine your using, the higher end ones can have anywhere from 5000/10000 polygons per model( Its usually double in terms of triangles, so it would be 10000/20000 triangles using the example above)

Whenever I create a model I find a halfway point since I prefer to model lower poly models to begin with. Once I have textured it, I then continue to build the higher model from that one. It can be done in reverse, but its a hell of allot more work and more complicated to optimize once you have too many faces to deal with

well, for the 3drad is the polycount thing, can say, simple: lower as it gets, ideal would be few shoeboxes without textures, no features like bumpy maps, particles... 

tip: for the design of the ingame model could help a bit, what for type of game you wanna make. if there will be some player object close to camera for longer time (even permanently), it should me more detailed. if there will be targets, they do not need to be close to camera, they can be less polycount with, smaller mipmap textures...

also, if we need a nice looking model, lot of things can be done with transparency textures, instead of model it (car grill, wheel spokes, tree branch, fence bars... etc.)

also LOD usage can help.