The translations of машини
were only "Car", "Cars".
But should I report it since "machines" was also correct?
Yes, "machines" should be accepted too, it's worth reporting it.
How about "The people like cars"? Is it a correct translation (or is it correct English at all)?
The people is not very correct because you are talking of people in general so you don't say "the people "such as you don't say "the cars"but "cars"
I did not hear her palatalizing the t at the end of "люблять", is that how it works in 3rd person plurals?