Pilot inbound to airport reported a NMAC with an aircraft passing above them and then the pilot reported doing a 360-degree turn because of concerns of another aircraft overtaking them from behind.

Narrative

Following contact with RHV Tower over the landmark known as 'UTC'; we began a straight-in approach to RHV Runway 31R at approximately 85 knots groundspeed and still in level flight at approximately 2;500 feet MSL. Thereafter we began a very gradual descent while I was giving instruction to a student-pilot on how to perform the straight-in approach-to-land at RHV; referencing landmarks and descent timing; when we were overtaken from above and on the right-hand side by Aircraft Y that appeared to come within 75 feet of our airplane; both vertically and laterally - the encounter occurred just abeam the landmark known as 'Mt. Misery' relative to the straight-in approach; (identifiable on the SFO terminal area chart). The intruding Aircraft Y overtook our airplane by at least 10 knots and continued to descend below our altitude. An ADS-B traffic advisory alerted us to the conflict just moments before the encounter; significantly distracting my student during the straight-in approach; requiring me to take the controls. We did not hear any transmission from the RHV control tower that this traffic conflict was imminent. At the same time; there was another airplane behind us [Aircraft Z]; which I recall hearing during subsequent RHV transmissions to have been a tailwheel aircraft; that had a 30-knot overtake of our airplane; and was therefore instructed to perform a right-hand 360 degree turn for spacing. The RHV Tower did not inform us directly of this airplane; and I was unaware of its altitude; as the ADS-B did not alert us about this second airplane. Given the significant distraction and uncertainty of the position of the airplane behind us; I decided to break off the straight-in approach just past 'Mt. Misery' (identifiable on the SFO Terminal Area Chart) and immediately began a steep-climbing right-hand turn from about 2;100 feet MSL; in order to repeat the straight-in approach procedure in the interest of safety; stability of the approach; and for the benefit of my student. The RHV Tower then asked us 'what are you doing'; to which we replied we were circling back to re-establish ourselves on the final approach to Runway 31. The RHV Tower then stated that we should have informed them as to our intentions before 'maneuvering'; which I acknowledged. It was unclear to me whether having broken-off the approach created a conflict with Aircraft Z behind us; as we were not informed of their altitude at any time. The second straight-in approach and landing was then performed after circling back overhead Mt. Misery to re-join the straight-in approach to RHV Runway 31R without incident. While it is apparent to me that I needed to inform the RHV Tower of my intention to break off the straight-in approach even though I was outside of the RHV airspace; I believe there was inadequate separation provided by the RHV Tower about Aircraft Y that overtook us high and from the right; as well as the overtaking Aircraft Z behind us. I believe there was also inadequate control of the sequencing of the two other planes; given their significantly faster speed relative to ours. In the future; I will query the RHV control tower before breaking off any straight-in approach-to-land; in case there is any ADS-B traffic alert; traffic that is un-equipped with ADS-B or otherwise unseen; that might be overtaking us on straight-in approach to Runways 31 at RHV. End of statement.