Important to know for everyone, is BitCore a fork of Bitcoin, or is it a completely new coin that only used the bitcoin keys?
Bitcore is a new coin and use only the Bitcoin keys. That's the reason, Bitcore call it a virtual fork and not a real fork from Bitcoin. Also Bitcore has a smaller blockchain, bigger blocks and other features, that Bitcoin not has and you dont need to download the old, big Bitcoin blockchain (like in real forks from Bitcoin). More information about Bitcore you can find in the first two posts here in the thread.

Do not understand. It will not be a separate token with a separate purse? What problem does he solve in bitcoin?