Using Lumia 950 Windows 10 Mobile if I do a hard reset would that remove any software updates applied on that phone.
OS and firmware updates are not removed by hard reset. The versions listed in Settings -> System -> About will be unchanged.
Apps are removed by the reset process, and will be restored to the version included with the phone's OS build (for built-in apps) or currently on the Store (for apps restored from the Store). Note that apps which are no longer available in the Store cannot be brought back, and if you have any apps you were avoiding updating for some reason, you'll get the current version instead.
If you want to re-install old firmware / OS version on your phone, you'll need to re-flash the phone. The easy way to do this is the Windows Device Recovery Tool (WDRT), which will automatically grab an appropriate firmware image for your device. WDRT is a free download from Microsoft and runs on (desktop/"normal") Windows. The alternative is to manually find firmware files and use some command-line tools (which ship with WDRT, so you may as well download it anyhow) to manually flash them. The latter approach has the advantage of being able to choose which version(s) to flash, assuming you can find the files.
I would say so, since a hard reset would set your phone back to factory settings. According to Microsoft: "Resetting your Windows phone will return it to the same state it was in the first time you turned it on. All of your personal content will be erased, and the phone will be restored to its factory settings." (source). According to the bottom of this article firmware updates would stay though. Make sure to backup your phone in case you plan to restore your settings and apps. There is a link on how to do that on the first link.