This is an interesting post here and I believe some of the questions had been raised before. Here are my thoughts:-
1) Is it fair to say that all schools and lineages of Buddhism would have its share of highly attained masters, which are in reality manifestations of enlightened beings?
- Yes, I believe that all authentic schools of Buddhism would have its fair share of attained masters who are qualified and able to guide others. However, I do not believe that all attained masters are necessarily emanations of Buddhas. There are masters who have achieved great attainments through the merit of their own spiritual practice. However, there are quite a few masters who are also great emanations of enlightened beings too. So, it doesn't really matter if they are emanations or not but whether they are qualified to teach and guide others or not.
2) Is it correct to say that an enlightened being can reincarnate in the Buddhist school/lineage of their choosing? ie previous life - Mahayana, next life - Hinayana and so on?
-Yes, they can emanate back and forth. Lama Zopa's previous life was a great Nyingma meditator and one of Kyabje Trijang Rinpoche's previous life was recognized as the Karmapa and he held the seat of the Karma Kagyu and was well-respected. However, most Tulkus choose to return as custodians of their previous life's lineage so the special teachings could be preserved and propagated.
3) Is it therefore, correct to say that such enlightened masters may then also choose to reincarnate as teachers of other religions - christian, hindu and so on?
- It is possible for enlightened masters to emanate out as teachers of other faiths. They would emanate for the sole purpose of leading that group of people towards finding a path. I believe that Mother Teresa was definitely an emanation as she has helped so many poverty-stricken Indians. She continues to inspire people till this day although she has passed away. I am not clairvoyant but that seems to me, the actions of a Bodhisattva.
4) If that is the case, would it be possible for other religions to lead you to enlightenment? Is Buddhism a label that applies to a certain set of people, and another religion lets say Christianity, also a form of Buddhism for a different set of people? Could it be possible that Christianity and Hinduism are just a part of the 84,000 teachings that Shakyamuni Buddha laid down for the people of today?
- Yes, all religions preaches the virtue of moral conduct. However, it leads you halfway but does not bring you all the way towards enlightenment. Buddhism is specially designed with its many levels of mental capacity in mind to help bring you towards enlightenment. That doesn't mean all Buddhists will reach enlightenment in this lifetime or those of other religions cannot reach enlightenment. Everybody has an equal chance but it is faster and quicker if you knew the path or you knew someone who could lead you there. That's the major difference. On the other hand, Christianity and Hinduism are not a part of Buddha's teachings. They do share certain similarities but they are very different religions and with different founders.
5) And is Buddhism just a label for us, and in the reality of things, there is no separation between Buddhism, Hinduism, Christianity as all have the power to lead you to the ultimate state?
-Yes, i believe you are right. Religion is just a label after all. Calling oneself a Buddhist and performing its superficial rituals does not bring you closer towards enlightenment than a Christian or a Hindu. However, in Buddhism, there is a greater amount of teachings that point the way our mind works and teachings that guide us step-by-step towards enlightenment. It is up to us to follow it without getting caught up with the labels and rituals.