Why there must be a station connected to the AP in order for you to establish a handshake
Let me try to explain this: You're not establishing a handshake, you're capturing one. A successful handshake is generated when the client has the right key for the AP, and that's what you need in order to crack the WPA key. That's why you need to have a client connected to the AP, so that you can deauth (much like "kick") that client, which in turn will try to reconnect and will generate the handshake you're looking for.
Also what's wrong with the laptop's wifi adapter?
There's nothing wrong with them (apart from them not working with virtual machines, which is normal), but you have to keep in mind that they are not as powerful as, say, a Alfa adapter. Sometimes you may catch an AP with connected clients, but the AP is so far away that the card won't be able to efficiently communicate with the AP/deauth clients. That's when a USB card with RP-SMA plug + a good antenna becomes handy.