Can anyone tell me if Magento Patches are cumulative? In other words, does installing SUPEE-5344 also resolve SUPEE-4829 and so on, are do all of relevant patches have to be installed separately?
Patches are created when a developer working on one version makes an update to a new version (in layman terms). So no, they are not cumulative. You will need to install all patches in the correct sequence and run magento between each install.
Each pach only patches exactly what it is described to patch, therefore you must apply each and every applicable patch for your version of Magento.
Start with the oldest one and move forward. View it like a module install, before applying, disable compilation, then disable and clear the cache. After testing, give the cache another clear and then reenable. Recompile and only afterwards, enable the compiler.
Also, every time you upgrade from one version to the next, no matter how minor the version, you must reapply all applicable patches for the new version you installed. IOTW, Magento suffers regression errors every time you upgrade. You must for example, patch for the XMLRPC hole until you reach a version where it has been applied to the source code and become permanent.
Thank you both for your detailed and prompt responses. Very much appreciated.
Follow up question if I might. What if I added the patches in the incorrect order? I had seen the urgent notice to install SUPEE-5344 and did so prior to seeing the other patches. I then installed SUPEE-4829 prior to seeing your responses. Do I simply reinstall them in the appropriate order? If not, how does one "uninstall" or revert the patch?