if i remember correctly, we were shown the back of the head of the woman who was having the affair with richard. i certainly didn't think it was in any way implied at any point that marta was the other woman. i make no claim to catching every detail of a film, & there was so much detail in this film that it's easy to believe something got past me, but i don't recall such a thing being shown or implied.
& the same would go for the inheritance. as i recall, we only know that harlan does not want to leave his estate to his family, for the reasons the film took the time to lay out: they were shifty, unethical, ungrateful, not deserving.
the film takes pains to show marta as a sweet, pure, uncompromised person who can't tell a lie without getting sick, so doing those things would be against the nature of the character as she's shown to us.
Correct. Besides, the woman photographed next to Richard seemed more Asian in appearance.