Will the pre-loaded version of Office 2010 that I purchased with my laptop still work and be supported if I install the free Windows 10 upgrade?
Will I need to re-install office after the upgrade?
Office 2010 should work with Windows 10 from what I have been reading. I cannot say for sure if you will need to reinstall it after the upgrade. I would like to think it would keep your installed software when upgrading.
It should work fine after the upgrade, ensure you have your product key and installer just in case you ever want to perform a clean installation.