To begin with, as I am sure you are aware, body cameras on law enforcement is a very new and rapidly evolving policing technique. As a result, there are very few rules on the books, and even fewer (possibly none) cases that have discussed body cameras. However, it would stand to reason that the rules and laws applied to similar recording (like dash mounted cameras) would carry over to body cameras.
As for your first question, may an officer start recording you 15 minutes after a stop without telling you, it stands to reason that the action would be allowed. The underlying rational behind this is similar to dash cams. The purpose of the camera is to record the occurrence independent of what the officer and the arrestee is doing. For example, you may or may not know that during a traffic stop, the squad car is recording the incident. However, that has no bearing on how you act and say what you say. Again, after conducting research, as I initially presumed, there is no law addressing this topic.
As to your second question, what happens to the portion that is not recorded depends on the circumstance. If it is irrelvant to the incident (i.e., asking for proof of insurance or just running your driver's license) there may be minimal to no repercussions against the officer or the State that is prosecuting you.
However, if these 15 minutes are relevant and material to the charges the State is trying to prove and you are defending against, a skilled attorney may be able to persuade the Court to exclude the officer's testimony and observations during this 15 minute period. To help understand this, consider the example below:
-You have been stopped for DUI. The officer has you perform certain tests (standing on one-leg, counting to a certain number, walking in a straight line, checking your pupils). These tests were done during the 15 minute period the camera was not recording. The rest of the stop and arrest was recorded. You hire a lawyer who issues a subpoena for this recording, but the State and the police do not produce it. Your lawyer may be able to ask the Court to sanction the State as a result of their failure to produce this video (or the portion of the video showing the tests.) As a sanction, your attorney persuades the judge to prohibit the officer from testifying about how you performed on the tests. Without this testimony, the State would have difficulty in obtaining a conviction against you for DUI.
Because this is a very new topic that does not have many laws, procedures or regulations overseeing the use of the cameras, it is difficult to give you a concise, straight-forward answer. However, based upon my knowledge and experience, these would be my best conclusions.
Please let me know if you have any follow-up questions that I would be more than happy to answer. If not, please leave positive feedback so I may receive credit for my response. Thank you!