Some people struggle with who/whom but in fact it’s the same as “he” versus “him”: if you replace “who” with “he” in the sentence and it sounds wrong then you should be using “whom”.
And the latin case is made muuuch more extreme due to the fact that we read poetry and stuff written in the yambic hexameter, which would have also been quite alien sounding to an average roman citizen on the street.
Word order does matter a bit in Latin, but much less than it does in English. "Dog bites man" and "man bites dog" are different due to word order. In Latin you can write "canis hominem mordet" in _any_ order and have it mean "dog bites man" because that's the only thing those nouns in those cases can mean. To do "man bites dog" you have to say "homo canem mordet" (again, in any order). Conventionally, though, you end a sentence or a subordinate clause with its verb, and the subject that matches up with a verb is usually the one closest to space-wise.