As @Lin-Buo-Ren says, it only works for metered connections, but you can use the snap set system refresh.timer= command to hold back updates.
Yes: Chrome (on Windows), Firefox (on Windows), Chrome OS
Can you prove this statement? Personally I quite like automatic background refreshes, it means my software is fresh and secure on any version of Ubuntu (and some other operating systems) without me needing to do anything! 
The snappy store is not open-source, everything else is. If you’re a developer and know Go then you’re very welcome to fork snappy to implement the changes you want (it’s licensed under the GNU General Public License v3.0 and the source code is available here). Indeed, some work has previously been done on implementing an alternative store (to resolve the perceived issues raised regarding External repositories).