What is the difference in doctrine and practice between Tendai and Zen?
Doctrine: Not much difference between mainstream Zen schools in China & Korea, or the Rinzai school of Japan. Soto Zen's a bit more unique. For our purposes, though, they're very close cousins... much Ch'an and Zen doctrine comes from the Tiantai school of China, which is where Tendai comes from too. Practice: again similar, but there's greater variety of practices in Tendai than in any Zen school. Two examples of this are Mikkyo and Kaihogyo. Mikkyo is Japanese Vajrayana (like Tibetan Buddhism); Kaihogyo... is really something special.
Do you think that a mystical experience requires ignoring scientific facts and requires a belief in religious myth?
No, I think that would be stupid. Mystical experiences are phenomena like any other. I'm not interested in mythmaking except as a means to an end, an upaya.
Is the mystical experience more valuable than observable facts?
No, a mystical experience is an observable fact (a fact of observation, a subjective experience of a specific kind).
After all, you could attain a mystical experience (an altered state of consciousness) by taking peyote, LSD or undergoing sensory deprivation. You don't have to believe in religious myth.
I'm inclined to agree, although I'm not convinced that all insights are of the same nature. Or better put: mot all paths necessarily lead to the same place or in the same way. It's easy to get lost in a muddle, and generally people get along better if they find a path that works for them and dig deep into it.
What is your definition of religion?
Religion is a social institution, like the DMV or any other kind of bureaucracy. It's neither good nor bad in itself. You can do helpful things with it, though, if you operate in good faith and with good guidance. Like a school: you can find means there to be useful to others, and less harmful. Different religions, like different bureaucracies, offer different tools to accomplish this. Some of them overlap.
However, traditions of practice persist in institutions. This is how we make the coffee. Here is how to load the truck. The same is true in religious institutions: this is how we alleviate anger. This is how we support those who are hurting. So there are different levels if you will: a doctrinal or theoretical level, a social or institutional level, and a practical level where productive work can happen.
How is Tendai different from Pure Land?
Pure Land is a practice. It can be found in all Mahayana cultures: Tibet, China, Korea, Japan, Vietnam, all of them. Some schools include Pure Land practices, like one color in a spectrum. Others make Pure Land practice their entire focus. Tendai includes Pure Land practice, significantly. Some Tendai priests do Pure Land practice (nembutsu) exclusively and intensively. Some do it hardly ever; their emphasis is different. For instance: my teacher, Monshin Naamon, is primarily interested in seated meditation. That is his main practice. He also does calligraphy, nembutsu, academic study, and a host of other things. But seated meditation has been his main practice. By contrast, the head of California Buddhist Monastery, Keisho Leary, is primarily an esoteric (Mikkyo) practitioner. He also does Kaihogyo-style practice around the mountain at his temple. Both approaches are fully Tendai. There is much room to find yourself in Tendai, to find a way that is right for your needs and talents.
Thich Nhat Hanh says Pure Land emphasizes seeking salvation from what appears to be an external source. What I understand so far of "real" Buddhism is what the Buddha said when he was dying, "Be a lamp unto yourselves," that the Buddha is already within us. So should we ultimately depend on ourselves or an external source?
This is a great question. The Buddha we seek is not outside ourselves. Where would you look for it? In the Ekayana teachings, our emphasis is on the Buddha-mind within. The enlightened qualities of Amida Buddha are latent within us, as potential. Through practice and attention, we begin to manifest those qualities. That is all. Think of a river backed up behind a beaver dam. If someone methodically breaks the dam, that potential energy of the water is expressed in a rush, a flood. That metaphor might help. I repeat: no Buddha is real until you see it for yourself. When Amida manifests himself to you, it is your enlightened qualities that manifest themselves to you. Nothing "external," because there is no in or out; no corners, no center, no edges. To put it in Thich Nhat Hanh's terms, our practice is to reach out and touch it. Of course this begs the question: what is a "self" in Buddhism again? Where does a self start or stop?