in sopken everyday English, 'coming' (which I answered) and 'arriving' are synonymous
However, they are different words and have different meanings, as they do in french.
They are somewhat different but there is sufficient overlap that it is common to say "J'arrive" for "I'm coming" as one might call out to someone from the next room. So it's no stretch to use it that way here.
Non. English requires an article (the) here. The use of « 's » with a noun indicates possession, not a contraction with a verb. You would say "The car is arriving".
Whilst I agree with the need for an article, in Australia we very, very regularly contract 'noun + is'. 'My wife's coming home tomorrow', etc - very, very common.
Vehicle is 'véhicule'; so for vehicle to be right the phrase would have been 'un véhicule arrive'.
Depending on the context, "One car arrives" is also a correct translation of "Une voiture arrive".