When it comes to answering emails, I agree with silkroute. I would say it’s pretty common to answer emails. For example, when I came back from a vacation I had about 400+ emails and I hired a VA to go through it. I simply didn’t have time for it and most of them were pretty much FAQ cases. Although you need to be OK with the content and buyer needs to set up an account for you. You can’t send it out from your own email account and email signature should indicate that you are representing the company/buyer.
However, I think purchases are a little bit more complicated for Fiverr VAs. You don’t have a contract that would outline what exactly are you authorized to purchase and I doubt any of the buyers would give out company’s credit card details and such. VAs wouldn’t pay out of their own pocket and a buyer who gives their payment method access to a five dollar VA doesn’t really care about security.
So, I think sending out emails is fine as long as you do your research and you approve the content. However, I would not recommend making any purchases if Fiverr order is the only link between you and your employer.