RNA test is not meant to be diagnostic, and the 4th generation test needs to be taken at 28 days (or anytime thereafter) to be considered conclusive. However, chances are high that you do not have HIV given the negative RNA.
It does. It has some false positives, and also, the timing of the detection of the virus itself can vary. So, maybe 12 days was long enough, and maybe it wasn't. Unless the person you were with was confirmed HIV+, this would not be an event that personally concerned me enough to test further.