I hope this message finds you well. I am a licensed IP attorney with over a dozen years of experience. It is a pleasure to assist you today.
The answers to your questions are yes, and yes.
You do need to file a copyright on Countdown. Though Countdown is a derivative of your original work, the fact that it is named differently alone necessitates that you also copyright that name. This does not do away with the previous copyright, but your new filing will only add to your IP holdings. Legally speaking, the first copyright will only serve to strengthen your claims to the second one.
It would also serve you well since this is a business opportunity to trademark the name relative to your game. Like Copyright, this can be filed on-line and is not extremely difficult. I suggest you give it a go yourself and if you feel overwhelmed, you hire an attorney. It is a pretty simple process though.
Once you have received a copyright and trademark, you can then seek international protection on those IP rights well. I would recommend hiring a seasoned IP attorney to handle those filings for you though.
Remember, by filing for this protection, you are not only protecting your IP, you are adding value to your business. If you were to sell, this is valuable to have in the overall portfolio.
Let me know if you have any other questions or comments. Please also rate my answer positively (THREE OR MORE STARS) on the ratings bar on your end.
Thank you and best wishes!