My question is - if I buy one of every trap element - can I trap every villain with it? I mean I know I can only have one villain at a time, but can I re-use the trap to trap a different villain when I am done with said villain?
Yes. When you trap a villain using an "used" trap it will ask you which you want to keep in the trap and which to send to the villain vault. It won't affect the evolved state of a villain either (as long as you don't put the villain on another trap of the same element, evolved state is tied to the trap and will appear whenever that villain is on it)
Although you technically won't be able to buy "every" element currently (light and dark traps aren't out for the ??? elements) but you will be able to trap every other villain (plus Kaos if you buy the Kaos trap)