In FNVEdit, in the mod's File Header section it lists its master dependencies. Only remove a master if it's actually not being used by the mod else stuff will break.
As for the stuff being ticked in the editor, it's because of the .NAM files that correspond to those mods that are in the data folder. If you delete the .NAM files, the GECK will stop having them checked by default, but Steam will redownload them eventually. The two real options would be to get used to unchecking them everytime, or to write a NVSE plugin that alters the GECK to disable the .NAM file check.
Queue
Edit - Oh, or you could probably hex edit your copy of Geck.exe to disable the .NAM check. Keep in mind I haven't tried this so don't know if it'll work, but you could open up Geck.exe in a hex editor, search for .NAM and change it to .___ (or some other dummied out file extension). The more complicated way would be to find the actual code that checks for the .NAM file and NOP it out or jump past it, but that's as complicated as the NVSE plugin approach.