Certainly the Aristotelian description formed by Aquinas I think would differ. It also differs significantly from the Eastern Church, which was never contaminated by Aristotelian philosophy. That being said, they did all believe in the Real Presence, under different terms and descriptions.
This is a reference to the Apostolic Succession. The valid Eucharist was considered that which was united with the Bishop. The celebration of the Holy Mysteries by those who were not in unity with the Bishop was considered to be invalid.
No, but I do not use those as theological sources who do not share the One Faith.
The risk is, if you use their writings to defend a position, and they depart from the One Faith, then eventually you will get caught up in their departures. Tertullian is a good example. He wafts in and out of orthodoxy!