Is this word related by any chance to Russian "среда"? I have seen some words which look surprisingly similar, like szomszéd and "сосед". The first one could be an adaptation of the Slavic root, or the other way round, although I think there must have been a Slavic substratum in the area before the Hungarians moved in (of course, there we get into controversial material). Any ideas on this?
Yes; Hungarian has quite a number of borrowings from Slavic, including half the weekday names (compare csütörtök "Thursday" and péntek "Friday" with Slovak štvrtok and piatok, for example). I'm not sure which Slavic language(s) those loans come from (or whether the languages were even as separate at the time of the borrowing as they are now).
With those weekday names, I think the direction of the borrowing is pretty clear since the roots have meaning in Slavic ("middle", "fourth", "fifth").
Yes, correct. The names for Monday - "hétfő" and Sunday - "vasárnap" are Hungarian though. "Hétfő" means the head of the week and "vasárnap" means the day of the market. Not sure about "kedd" - Tuesday. The rest are of Slavic origin.
There are many words going both ways between the neighboring languages, naturally.