If you wanted to be very formal in English you could construct your sentences this way.
Colloquially, people often say "Where are they going to?", which places the preposition at the end of the sentence. Using older, Latin-style preposition-use would change this sentence to "To where are they going?"
As KruzKalke alludes to above, that "rule" was a Latinate imposition on English, popular during the era of Classicism. Germanic-language grammar is quite comfortable with prepositions occurring at the end of clauses, particularly in cases of phrasal verbs, ellipsis, and stranding due to wh-movement:
The rule is archaic. There's a nice discussion on the subject at http://itre.cis.upenn.edu/~myl/languagelog/archives/001702.html. The discussion mentions a great quote about this rule (as the discussion points out, almost certainly misattributed to Winston Churchill): " "This is nonsense up with which I will not put." Yes, yes, a preposition is supposed to precede a noun, but English absorbs many prepositions into fixed expressions, as in "I'd ask to stay for supper, but I wouldn't want to put you out." A linguist might even argue that out was not a preposition but a particle attached to the verb put in order to form a phrasal verb, but in any case the sentence is perfectly fine English.
I'm not a native Russian speaker, but I'm sure there is no such expression "Где они идут?". It's simply wrong. It has no meaning. If action or movement is involved, then you use the word 'куда' (Where are you going? / Where should I put this?). If you're asking the static location then use 'где'. Similarly, "To where are they going?" is simply wrong. Maybe it's an old form but it should be considered wrong. The proper equivalent English expression is simply "Where are they going?" Trying to translate word for word will cause you nothing but problems.
what about "which way do they go"? I'm a native Czech speaker, these two languages have a LOT in common, especially the words that sound almost exactly the same in both languages - I'm regularly doing new exercises and skills without hovering the mouse over the new word, simply because it's the same as in my native language. So, could it be right?
US English speaker - "Where do they go to?" sounds like it's asking for a response about an habitual action ("Where do they go to every Saturday?"), which is fine in English linguistically, but the Russian is specifically asking either where they are going now, or where they plan on going in the near future.
@Nishan_Paul - It looks like they accept both ("Where are they going?" is the default answer on my screen).
But in general, it's because English lost its different "wheres". We used to have one like the Russian куда (whither), and one like откуда (from where - whence), but over time those became less popular and just replaced by the one "where". But, "where" can also refer to a general location ("Where is she standing?"), so it also became normal to attach a preposition to specify what kind of "where" you're using.