Should a violinest use a hand exerciser, by which I am referring to the kind generally used by guitarists? An example of one may be found here.
If so, is there a specific kind and/or tension which is ideal?
Hand strength is important in the violin, but so is fine motor control. Why not develop both? Practicing etudes by Kreutzer (42 Studies) and Paganini (24 Caprices, Op. 1) should strengthen your fingers enough to play almost anything. Try chord and trill exercises for a serious finger workout.
Here is a graded list of etudes.
The answer to this one is 'it depends on you'
I never felt the need to use one when playing violin, as finger strength was never a requirement, but I do use one now I play guitar as for certain songs I need the extra strength and stamina to hold complex barre chords.
If you feel you don't have the strength or stamina to be able to play the pieces you want consider getting one and seeing if it makes a difference.
I've never known anyone who has needed to use hand strengthening exercises in addition to normal practice to gain enough strength to play properly - usually the strength needed would come with the regular practice required (and both of these will come gradually, you're not going to be bashing out Paganini's caprices on day 2.) Perhaps if someone had weak hands for a particular medical reason this may be necessary, but in general I'd say it's just not required.
For guitarists the need to hold barre chords and the like much earlier in training means that yes, strengthening exercises could well be necessary - I'm not proclaiming that they're not necessary on any instrument, I just speak for the violin.