First, the bad news. Your copy of CS6 is almost four years old. It will never be updated. It's not supported under OS X El Capitan.
Many others have reported problems with InDesign CS 6 in El Capitan so it's not particular to you. You can try restoring InDesign preferences but that may have no effect at all.
You should probably either roll back to an earlier OS version, or accept that you need to update to Creative Cloud.
We are now seeing this in our environment as we upgrade from 10.9 to 10.11.4.
We have Universal type client 6.0.2 installed and managing our fonts, and El Capitan has an issue with PS fonts / with Open type fonts already.
Pushing us tot he creative cloud isn't feasible for Enterprise organizations yet. It would cost our business over 4 million to upgrade.
** Try clearing out all your adobe font lists, and font caches - and see if that helps to resolve your issues.
Then, as Steve says, roll back to an earlier O/S or do not upgrade the machines that have haven't been.
Unfortunately new hardware cannot take Older Operating Systems, hence the problem with Adobe's lack of support for CS6.
Sorry, but you’re going have to live with some of these issue then. You can’t expect an application to be supported forever. CS6 is now more than 4 years old and 3 full versions out of date.