Likely is pulsatile tinnitus. The pulsing or rhythmatic sound matches the heart beat. Usually the cause cannot be determined but some are caused by a narrowing of an artery near the inner or middle ear. It is highly unlikely to to be a precursor of a stroke or a symptom of an aneurism. If it is bothersome, see an ENT with some specialization in tinnitus.
Sounds like you should discuss with a doctor.
Do you measure a irregular rhythm, high or low pulse rate or have any blood pressure problems?
There's nothing in what you say that makes me think: stroke or aneurysm. Did you find somewhere that the problems you listed are associated with stroke or aneurysm? If yes, then please don't take me as an argument against the other reference.