1)
If you bought a retail copy of Office (meaning it was not already installed when you bought your computer, you bought it later), you can install on two machines.
And yes, you can install on a new machine. It may take a phone call to Microsoft to explain that the old machine is dead.
2)
If you have an OEM version, (shipped with a new PC), or your PC came with a free limited trial version, and you purchased a license, your license is limited to that PC.
Microsoft Software License Terms for Microsoft Office 2010