Can utilities like Chkdsk or Defrag be run on an open container?

You can run any disk utility on BestCrypt drives exactly in the same way as you run it on other regular drives.

It is safe to run defrag utility on BestCrypt volumes, but if you are going to run the utility on the hard drive where BestCrypt containers are stored, it is strongly recommended to dismount the containers (if they are mounted) before running the utility.
Besides, if you want the container file to be defragmented like any other files, you have to disable Container Guard Utility. If it is active, it won't allow defragment utility to move parts of the container file.