I forgot the password of my iCloud account. I'm using iPhone 4S I am afraid that if I updated to the new iOS, the phone will be locked and I wouldn't be able to use it. P.S. I have tried iForgot to restore my password, but it didn't work out as it keeps telling me that my answers are wrong.
Yes, you will be required to verify your account when you first log in.
I would suggest trying to get to the bottom of it BEFORE you upgrade, it will be harder after (since you should still have some access to email accounts etc).
Also, I would research the effects of running iOS8 on an iPhone 4S. Although it may be supported, I would think it would be incredibly slow.
I know you didn't ask for the second part of this answer, but I would strongly recommend you do some more research on this before blindly doing it.
Yes, the iCloud password is required after an upgrade to enable iCloud on the device.
If you are providing answers you believe to be correct, and the iForgot system is not recognizing them, you will need to contact Apple directly. Start at the Contact page for Apple ID support to determine the appropriate contact method for your country or location.
I would suggest you recover you password, since you will need it in the future.
Go to Apple website to recover it.
The use the email option to get it.