Can the 'megy' go at the end of the sentence or does it have to be between the two places?
I second this question! This reminds me of another sentence in this course, where somebody goes "utcáról utcára." The verb came after those two words.
Yes, it can be 'A postás Tóthéktól Szabóékhoz megy.' for sure.
Continuing the vowel harmony question, does the postposition always agree with the name (and not the -ék), which is why we have Szabóékhoz and not Szabóékhez?
The é is really neutral as far as vowel harmony, so yes, it has to be decided by the rest of the word / name.
Are family names always made plural by -ék regardless of vowel harmony?
Right, the -ék ending doesn't harmonize. é is really pretty neutral with regard to vowel harmony in general.
It is a specific suffix meaning "... and company" or " ... and family". So this is not the actual plural suffix. That would be "Tóthok" and "Szabók". And yes, it is always "-ék".