No probs! Dealers use a very sophisticated version costing quite a lot of money but most peeps use the normal ones with sharpened ends. You can usually smell damp too so use your noses and if it smells musty run away!
It is good etiquette to ask lol, if they have anything to hide they won't be happy but otherwise providing you are genuinely interested and do it in discrete places they should be fine.
No not at all. You need to know you are getting a dry van and you would only damp test it when you are sure it is what you want. By that time any seller worth their salt with nothing to hide will be amenable to you doing it.