1) It depends on the operating system more than anything. Even for single core architectures, multi-threading can be supported, but the threads are not executing in parallel - The OS will context-switch between them.
2) Intel usually supports two-way hardware threading ( also called simultaneous multi-threading), where each thread is allocated a pipeline. So if you have a process with two threads they can both execute on the same core simultaneously.
3) See 1. Basically the operating system is going to allocate as many threads as it can to hardware before it plans to context-switch between the threads it couldn't allocate. This process is dependent on the OS's scheduler, and you can read about the Linux one to get a good idea of what's going on.
Edit: Hypethreading is basically the hardware threading feature I mentioned.