How will be cipher selected when client is running on version TLS 1.3 and server is running on TLS 1.2? How will be cipher selected when a client is running on version TLS 1.3 and server is running on TLS 1.2?

The cipher list provided by TLS 1.3 client will be different than the version supported on the TLS 1.2 server.
If the client is only supporting TLS 1.3  or only TLS 1.3 ciphers the SSL handshake will fail. Otherwise the cipher will be selected as it is usually done with TLS 1.2: the client shows which ciphers it supports in the ClientHello and the server will pick the one which a) is supported by the server and b) fits the type of certificate of the server (i.e. authentication RSA or ECDSA). If there is no common cipher the handshake will fail.