A online bank account was set up for me...
Why was it set up for you? Why didn't you set it up yourself? Were you expecting this to happen? What is the source of the funds? Was it money you were expecting to receive?
...with a bank called cornerstone bank...
You don't indicate the country, but there are several banks that go by that name in the U.S. You can search with the FDIC to see if there are banks that have that name. My search for that is here; I strongly suspect that the "bank" they sent this to "money" to won't match the details on any of them, but you can check if you'd like. There are probably equivalent sites for other countries.
I was told before I could transfer any money or have access to the account that I needed to pay a fee called account activate plus stamp duty charge
Whether the stamp duty applies depends a little on the country, but my understanding from this is that countries that have this will usually apply it to things like firearm sales and property transfers, not to opening a bank account.
I've never paid an account activation fee at any bank that I've done business with. Banks may have an account maintenance fee if you don't maintain the minimum balance or activity requirements, but they typically won't have one for opening one in the first place.
Also, the only time where I had to pay a fee to receive money was when I was receiving a wire transfer, and the person who was sending me the money simply deducted the fee from the amount that they were sending me - I didn't have to send them other money.
This is a classic setup for an advance-fee scam. If you pay the fees, they'll likely either come up with more fees that you supposedly need to pay or disappear with the money you gave them.
Note that, if you did pay them money, sometimes "recovery experts" will contact you promising to get your money back. This is another scam to try to get you to pay them even more money.