Can my chain of command stop or mess up my MEB?

The entire NCO Support Channel and Chain of Command should be tracking your MEB. He is likely asking just so he knows your status. Remember that the CSM is responsible for your health and welfare, and is also responsible for making sure you get the proper care AND the proper training within your medical limits. It is incumbent upon him to know what your status is, as well as your limitations. And... when the time comes, he is also responsible for making sure you get out of the Army without a hitch AND replaces you in a timely manner.

Don't read into it. CSM is just doing his job.

Your CSM is simply tracking your progress, he and the BN Cdr. receive weekly updates during staff call, the fact that he is inquiring is a positive thing. Whether he is encouraging/coaching your COC, or simply thinks you are worth the extra effort. Stop an MEB, not at all, there is only negative effect that would come from a COC trying to influence the process.

I have seen this happen before. I have had to track several Soldiers about their MEB. The issue is that sometimes the Providers are not given the information so they don't know where you are in the process. There are regulations on the timeline of the MEB. They are most likely making sure that is it happening in a timely manner.