What is the Buddhist principle of "justice"? Does it have one? And how is it related to the notion of the colloquially used term "karma?"
In what ways is Buddhism similar to Christianity?
In what ways does it differ?
Is it true that there are strands of Buddhism that is mystical and relies heavily on tradition and mysticism?
Speaking only for early Buddhism as I understand and practice it:
Regarding
justice: Justice is essentially kamma: results always follow causes. Are results and causes always proportional? Not in superficial appearance, at first glance. Other strands of prior kamma modify results too. E.g. There are innumerable causes that can join together to cause any effect. E.g. I plant (cause) a seed, I can reasonably expect a plant to sprout from it (effect). However, there are other additional causes that can combine together which modifies the resultant effect, e.g. mineral content of the soil, amount of sunlight, temperature, moisture, insects, etc.
Regarding
mysticism: There are elements of what could be called mysticism in early Buddhism. The Buddha taught the truth of what he personally experienced, e.g. deities, heavens, hells, etc. However, since faith is not essential for "salvation" in Buddhism, we do not need to have blind faith in these things. We are called to walk the progressive, graduated Path ourselves, in order to perceive these things directly ... not to believe on blind faith. It reminds me of an event where the Buddha was teaching a point of doctrine to his disciples. He asked his most senior disciple (Ven. Sariputta) if he believed in what he (the Buddha) was teaching. Ven. Sariputta stated "no" - he didn't believe, because he hadn't known it for himself - yet. The Buddha praised him.
Regarding
similarities to Christianity: Early Buddhism is similar to modern Christianity in that virtuous behavior is enjoined, and the golden rule is found in the early Buddhist texts. Metta (loving-kindness) is a virtue in Buddhism, similar to love in Christianity, but it is not considered the highest virtue.
Regarding
differences: There are also many differences: Buddhism teaches rebirth; kamma; a number of different levels of heavens & hells (all impermanent); self-help/salvation (based on the law of kamma); innumerable deities (powerful but not omnipotent, extremely long lived into the aeons but not eternal, and most live under various delusions of their own grandeur, lifespan, or power) - we are deities, in a sense, compared to those in realms below our own; etc.
More differences: I specifically chose early Buddhism because it focuses on the importance of intention (not the letter of the law), things to be known personally (not belief in unverifiable dogmas), that it possesses no intermediaries or hierarchies (vs plenty of them in other religions), that it doesn't depend on a "real" Buddha (vs religions which require a "real" figurehead which constitutes their foundations and must be followed blindly), and posits truths universally applicable throughout space & time (vs things bound to time/culture/lands/an exclusive people group/etc.), with an emphasis on less (vs more), that it also encourages independent thought (vs need for conformity), that it targeted dukkha/suffering, the root issue of the human condition (vs other religions which seek to treat the symptoms of dukkha), and that it provides a systematic, methodical, testable path to treat that condition (vs dogmas, again).
(P.S. Regarding
other forms of "Buddhisms", such as Mahayana, Tibetan/Vajrayana, Zen, etc. are later developments, and IMO they are all different religions, practically speaking. Early Buddhism is more
practice based, with an emphasis on personal knowledge and effort towards personal transcendence. Theravada, as it stands today, is one expression of early Buddhism but tends towards more
study instead of practice. Mahayana is essentially
faith &
devotional-based with savior figures, like the Abrahamic religions, and is largely founded on texts written hundreds of years after the early Buddhist texts. Vajrayana/Tibetan (Dali Lama) is for the most part Mahayana + native Tibetan shamanism.)