As long as they are legally allowed to be sold your region, you'll be fine. Do note that many gateways may consider vape pens to be high risk so that can restrict what ones you can use.
Yes. However Shopify will not provide their merchant services to E-cig sites. Many merchant providers won't. I own ViceVaporLounge.com and have been with Shopify for a year. I've got a great merchant provider that I can recommend if you still need one.
That's a great question.
I've located a payment gateway company that does deal with online merchants selling Vape Pens and e-Cigarettes. They're called Tasker Payment Gateways and their website is: http://taskerpaymentgateways.com. You can also give them a call at (207)772-8737.
I hope that answers your question! If you need anything else, I'd be happy to help!