I hope this imageExternal ↗ will help you confirm what you know.
Regarding your question about fixed stars.
From Azazel's Astrology "The following interpretations concern when a fixed star is conjunct a planet in one‟s chart or an angle or is prominent. Personal planets such as chart ruler/s and angles are important, with the influence of the fixed star being emphasized in both the life affairs and in the personality."
A fixed star if conjoined to one of the four angles is certainly important. As for the other cusps, I would personally say that the mere presence of a fixed star will most likely have no significant importance but it might be a supporting factor to consider when analyzing the house in question.