"The chair is always in front."
Translation:A szék mindig elöl van.
Elöl is (effectively) an adverb and it must have a verb with it - in this case, van does have to be there. A noun or an adjective can serve as the entire predicate without van, but an adverb (including positional expressions like itt, otthon, elöl, and so on) cannot.
A szék barna. (The chair is brown - adjective serving as the predicate.)
A szék egy szimbólum. (The chair is a symbol - noun serving as a predicate.)
A szék elöl van. (The chair is in front)
A szék otthon van. (The chair is at home)
A szék a víz alatt van. (The chair is underwater)
A szék rosszul van és haza akar menni. (The chair is unwell (adv.), and wants to go home.)
Is "van" strictly needed here? I thought it was supposed to be omitted in the 3rd person (check) singular (check) when you're just describing the subject (check). Is "elöl" somehow exempt from this?
Where should i put "van"? Is it wrong when i say "A szek mindig van elol?"
What is the difference, if any, between "a szék mindig elöl van" and "a szék mindig előtt van" in this kind of usage?
Your second version isn't correct. Előtt is a postposition and you use it in the form valami előtt "in front of something."
A szék mindig az ablak előtt van - the chair is always in front of the window.
A szék mindig az oroszlán előtt van - the chair is always in front of the lion.
A szék mindig elöl van - the chair is always in front (not in front of something but just generally in the front.)
Thanks for the clarification. One further question: is it merely incorrect for this example, or is it grammatically incorrect always?
That is, if asked: Van a szék az ablak előtt, vagy mögött? Then can I reply: A szék mindig előtt van.
Where az ablak is implicit (as would be acceptable in english) or is it simply wrong to omit the object of the postposition?
Basically, yes: it's wrong to simply omit it. You should think of előtt as if it means "in front of ...." and it is incomplete until you fill in the missing part. If you say A szék mindig előtt van. then it sounds about like "The chair is always in front of." would sound in English. In front of what? Incomplete.
A little more detailed answer is: If you want to say "in front of [pronoun]" - that is, "in front of me" or "in front of you", etc., then you place posessive endings on előtt as if it were something that could be possessed ("my in front", "your in front" etc.)
A szék előttem van - the chair is in front of me.
A szék előtted van - the chair is in front of you.
A szék előtte van - the chair is in front of him/her/it (and so on for us, you, and them).
So you can say A szék mindig előtte van, "The chair is always in front of it", where "it" refers back to something that has been mentioned earlier.