Tropical versus western Sidereal
I would like to answer this portion of the question.
While these astrological approaches use a zodiac whose measuring point or starting point is different, almost a whole sign of difference these days, I would suggest that the primary difference for the Fagan-Bradely school of Siderealists is in their practice of astrology rather than the fact that they use two different zodiacs. The Siderealists that I come into contact with use several different forms of charts and interpretive techniques. I'll list these with the understanding that I may or may not be speaking accurately for those in this diverse "school" of practice.
** Ingress charts. Siderealists often cite the Capsolar Ingress, where a chart is cast for the moment and place where Sun enters Sidereal Capricorn. I've used similar charts when doing Tropical Weather Charts such as those used in the system taught by the Church of Light. Siderealists cast these ingress charts for 0 Aries, 0 Cancer and 0 Libra as well, predicting national events and mundane happenings.
** Solar Return charts. I use these and the derivitive progressed daily angle charts almost exclusively. The Sun, at it's point of return, can be charted with specific angles in the chart. These angles progress at a regular rate between one solar return and the next, moving close to 1.25 degrees per day. Following where these angles are and the movement of the planets (transiting, natal and solar) with these angles gives an amazingly accurate picture of ones life. All of my predictive work is done with this method.
** Lunar Return charts. At one time I used to love these charts. Others still do. They show quite nicely the moods and responses to life that one will experience. I don't use these much now, having focused on the solar cycles.
** Fagan explored a number of techniques but I feel that thats just what they were --explorations. I've tried and dropped them.
Having pointed these few differences out, I think it only fair to state that I use a number of methods and have little use for other methods used by many astrologers. Its all part of my "if it doesn't work 100%, throw it out" theory.
For natal charts I use planets, aspects, house -- seldom use signs or even rulers, although I do use them sometimes. I use secondary progressions, solar arc progressions and mid-points. I love Marc Robertson's phase relationships and have used part of his work in my planet-series threads, although I have also done some different work with the inner planets and their different phases. Even in Sidereal practice, I seldom use houses, just angles and aspects and the planets in those angles. I have developed an interpretive scheme for solar return progressed angles that I don't think anyone is aware of -- its been quite helpful to me.
All that being said, I do understand and have used almost every astrological practice except Vedic, have studied with some of the best, and have had fun with astrology for some 35 years. Dave