Unfortunately after Buddhism began to spread it mixed with many of the magical thinking of the lands in which it spread, i.e. Hinduism, Tibetan and Chinese folk religion, and Shinto. Much of the Buddhism that has come to the West is heavily influenced by these things and you will find that a lot of people who are introduced to Buddhism are "tricked" into thinking that this is actually part of Buddhism proper.
Buddhism is fundamentally nontheistic or even apatheistic. Whether God exists or not is completely irrelevant as we are entirely unable to prove It exists or disprove that It exists and so there is no purpose to indulging in the subject except as perhaps a sociological/psychological subject.
Do some Buddhists believe that there is a universal consciousness and that reality is a relative illusion constructed by this mind? [etc.]
Some might do, but they are not unlike people who wear fursuits and imagine that they are living in some sort of 90s Disney movie. Most of the things you mentioned are completely baseless magical thinking coming from Hindu theology. This world is not an "illusion" and to think karma somehow governs our entirely lives from birth to death makes you a Hindu
how does Karma compare to a deistic god
Karma is a logical cause-effect thing. But as said before, in many circles it has become filled with a lot of magical thinking over time (i.e. one's soul becomes animals or whatever, which is originally a characteristic element in Hindu theology)
what are believed to be the writings of Buddha. I am having trouble finding a copy of core Buddhists writings on the Internet. I'm not looking for later interpretations, but what Buddha actually is said to have taught.
the Buddha never wrote anything himself, but his sayings are collected in works, some most certainly more accurate than others. Many later texts interpolated a lot of absurd mysticism and this is a big problem in Buddhism today. For example, the idea of "chakras" or chanting "om mani padme hum" as if Chenrezig (Avalokiteśvara), who was probably actually a Hindu deity, will apparently endow "blessings" upon us, and somehow its utterance will tap into the "vibrations of the universe" or some other nonsense. The best work you can read is the Dhammapada which includes none of this mystical wishful thinking that have crept into Buddhism over time.
do Buddhists view Jesus as another Buddha?
Why would we? Jesus said some nice things, but said that the fundamental imperative to one's existence was to worship God which is contrary to Buddhism.