It depends upon where you are purchasing them from. Online department stores such as Macy's Neimen and other are fine. However, purchasing new items from online auctions is always questionable.
Yes, you definately can. But only if you use accredited sites such as Bluefly and Nordstroms. If you get them from a real designer site, then they'll be real.
Buying designer brands on eBay or Craigslist is much riskier than buying online from Macys. Always check an eBay seller's reputation by checking their reviews and number of items sold.