It's a function of 32-bit versions of Adobe InDesign and a 64-bit install of Windows 7.x/8.x/10.
With the 64-bit version of Windows installed, it only puts 64-bit versions of software in the /Program Files folder. That's where Windows reaches into when it associates file suffixes to programs. 32-bit versions of software go into the /Program Files (x86) folder, which Windows doesn't reach into for file associations.
It stinks, but that's unfortunately the way it is. The solution is to use a 64-bit version of InDesign CC.
This is a Windows issue (and it has nothing to do with 32/64 bits). Reassociate INDD files with Indesign and you can again click the file to open Indesign.
This is a problem with the file association of your OS, has nothing to do with InDesign. As you did not write which OS you use, you have to reassociate the file type INDD, INDB, INDL, IDML, INX and INDT again with InDesign. Most propably with some "Open With …" command and an option to open this kind of file always with InDesign.
This is a problem which occurs often in windows. Sometimes, when installing a newer version, Windows is still pointing to the older version, which maybe deleted. Either try the "change default program" option or use a third party program, such as
Lot's of other solutions can be found on Google.