Yes, you can. You can use apps from play store that allow multiple profiles. There are many. On a rooted device you can use titanium backup and create a new profile for WhatsApp.
The official WhatsApp Web version doesn't support adding a new contact. But you can use some tricks with a third-party extension InTouchApp to add new contacts.
Go to Phone Settings-Apps-Whatsapp-Permissions. From here, enable Contacts, so that Whatsapp will get access to Phone Contacts and it will recognize the Whatsapp using numbers. If your number and new...