If a reinstallation of the software is needed, must I purchase a new license?
In general, no. If the same version of the software is reinstalled on the same machine or is not concurrently installed on any other machine, no new license is required. Additional licenses are generally required for installations above and beyond those allowed by the product's EULA.
If a reinstallation of the software is needed, is reactivation required?
Not always. If the same version of the software is reinstalled on the same machine and the hard disk is not reformatted prior to reinstalling, the software will remain activated. Reactivation will be required if the hard disk is reformatted and the software is reinstalled. This is because the software's activation status is stored on the hard drive and reformatting the hard drive erases that status.
What happens when you try to install and activate on more PCs than the end user license agreement (EULA) allows?
Per the EULA, installing on more PCs than the EULA allows would be in violation of the EULA. Technically, product activation does not limit the number of PCs the software can be installed on. It would be possible technically to install the software on, for example, 100 PCs. Activation would fail though on 99 (98 for Office XP or Office 2003) of those 100 PCs thereby limiting the usefulness of the illegal installation. Outside of an activation attempt, Microsoft does not know how many PCs Windows XP, Office XP family product, or Office 2003 System product have been installed on.