What would happen if you injected a human embryo into a pig?

Assuming the embryo would not be rejected, the fetus would develop as a normal human embryo. The mother's uterus has no effect on the DNA of the embryo, and there have been cases of human surrogate mothers giving birth to children with no genetic connection to the mother.

This wouldn't work, each species has it's own specific gestation, growth and development processes, and the pig's immune system would most likely attack the human cells once the foreign antigens are recognised.

It would be rejected and die. Simple.

Experts who are doing research on cloning (which requires a surrogate mother) claim that only closely related species can be surrogate mothers. For example, a zebra or a donkey may be surrogate mother for a horse, but not for a dog or mouse or bear or deer or vice versa. That means the scenario you describe is very unlikely.

Yup