Surprised that no-one has yet mentioned that VIIdim7 is a rootless (roll eyes) V7b9 chord. Many jazz players would consider that functionally there is no difference between V7 - I and VIIdim7 - I – if you have a functional cadence then any and all alterations are on the cards, to taste. Picking out whether the root is actually present or not seems like a somewhat unnecessary endeavour to my mind (perhaps I could be convinced otherwise) as musically I would say V7 - I and VIIdim7 - I are the same.
(eta: of course, one has the b9 alteration and the other doesn't, so it's that that I would focus on picking out. It should be quite clear as a jarring/jazzy/clashing/'cool' note)
That however provides an easy resolution to your third query, since in VIIdim7 - Imin, which I'm claiming is V7 - Im, the five chord is a dominant7, so has a major third (indeed this is the VII) whereas in Vm - Im the five chord has a minor third. As covered in other answers, if it sounds just like two minor chords one after the other, it's the Vm - Im. If it sounds like "dramatic tension! resolution to a minor chord" it's the VIIdim7 - Im.