Can my admin manage my iPad without me knowing? Can my admin manage my iPad (download programs, change settings, etc.) without me knowing? (Configuring it so that I cannot tell that it's managed.) 


My iPad is running iOS 12, and there are no messages in settings telling me that it is managed. It was set up and purchased by me, by the way. It's already connected to my personal Apple ID.

Edit: Can they manage my iPad if my only connection to them is that I'm signed into a managed Google Account (example@company.com) in Chrome? (sync)
You can tell if the device is supervised (i.e. managed) by opening Settings. Right at the top it says "This iPad is supervised and managed by xxxxxxx". If you do not have this message, your device is not supervised.

Your iPad cannot be supervised/managed merely by signing in to a managed Google Account in the Chrome browser.