Hi Joanne and welcome to SaleHoo
Sites such as DH and Alibaba are what is called B2B (Business to Business) directories. You have to always remember with these types of directories that they are just that, a directory. When you deal on Alibaba, you're not dealing with Alibaba itself, you're dealing with independent suppliers advertising on the site.
These directories can be great resources, but they can also be your worst nightmare. You'll find everything form genuine suppliers, fake makers and outright scammers who will take your cash, but never deliver a single thing. So it's really important that before you do any business with any supplier, you do your research on them.
In regards to Drop Shipping itself, these types of directories are more wholesale suppliers than Drop Shippers. However, it never hurts to ask a supplier if that is something they will do for you.
2 major tips
Never buy any branded products form Chinese supplier, at best you will be buying fakes (no matter what they will tell you) and at worst, you'll get scammed out of your money altogether.
Second tip, when you finally do decide you're happy to proceed with an order from a supplier, always choose a safe payment option. Credit Card or PayPal, never a wire transfer. A wire transfer is the absolute quickest way to loose your money!