What you say in the middle of your post is not entirely true. Mass is well defined.
It is an intrinsic property of any particle or object. Relativity only concerns space and time that are thus not absolute.
Special relativity is used for decades in calculations and it works damned well. A couple of predictions of general relativity have been recently observed in data and were still pending to be confirmed experimentally. On the other hand, it is good to keep in mind that the doors for alternative theories are still open. If I got it right, you mention one of these observations that are in agreement with general relativity predictions, don't you?
Maybe could you provide the sources where you read the info, so that I could have a deeper look and give more details?
RE: Einstein was right- Scientists proved Theory of relativity