Romwe is a fully functional site, but it's hard to tell whether it's actually a legitimate business. It's hard to say for sure, since there are so many online stores that sell a variety of things. Romwe has a website that works perfectly, but their Better Business Bureau (BBB) profile indicates that they are out of business.
If you order something from Romwe and need it quickly, don't expect it to be shipped out immediately. If you need an item within two weeks, it's better to shop at a US-based retailer. If you live in an area where delivery takes a bit longer, shop at Amazon.com or Walmart. You can expect to get your purchase within two or three weeks; if you live somewhere further, it will take longer.