Opposite of muj.

bIlugh is commonly used to mean "what you have just said is factually correct," but, as in the TKW phrase reH lugh charghwI' "The victor is always right.", it is also used to mean "what you just did (or are doing or about to do) is proper/ appropriate/ justified/ acceptable." (And, of course, likewise but in reverse for bIlughbe'.)

Asked: Can they be used for things? For example, imagine there are several switches on the wall. If you click the correct switch, the light will go on. Can I use lugh here?

No. As noted above, lugh isn't used exclusively when a person has made a correct statement. It is also used when an action can be moral/ proper/ appropriate/ suitable (or, with -be', immoral/ improper/ inappropriate/ unsuitable). In any case, it doesn't apply to light switches. 

A switch is never "factually correct" or "morally correct." A switch cannot be "right" or "wrong" in this sense - it can only do (or not do) what it's supposed to do or has been set up to do.

The switch that is "right" - that is, the switch that will do what it's installed to do - is the leQ mIt. 

Asked: Can they be used for phrases?

A: tlhIngan ghaH ghawran'e'

B: lugh mu'tlhegh./ lugh ngoDvetlh.

"That phrase is correct." / "That fact is correct".

I believe that this is NOT correct (no pun intended), because we have the verbs teH (be true) and qar (be accurate) which could be used here.

Your assessment is correct. bIlugh! 

Asked: In the meantime: is muj (be wrong) simply the opposite of lugh, and does it work the same way?

Yes. But, when referring to behavior, lughbe' is more common than muj.

Asked: Could one say leQ muj vI'uy "I clicked the wrong switch"?

See above. This would be leQ mItbe' vI'uy.

Asked: If "the victor is not right", is it the same to say lughbe' and muj? 

MO: Yes. But, as noted above, lughbe' is more common.