Tropical plants on Antarctica are no problem, once you accept that Antarctica wasn't originally on the south pole, but migrated there from continental drift (or Earth expansion).
The equator is fixed by our vector of angular momentum, which is pretty much unchangeable.
The Moon is attracted to all the mass of the Earth, not just the core. You need to learn about gravity.
Tropical plants on Antarctica are no problem, once you accept that Antarctica wasn't originally on the south pole, but migrated there from continental drift (or Earth expansion).
The equator is fixed by our vector of angular momentum, which is pretty much unchangeable.
The Moon is attracted to all the mass of the Earth, not just the core. You need to learn about gravity.