When browsing websites with Chrome sometimes I can see a green lock and encryption info inside. It says the connection with this website is 128-bit or 256-bit encrypted with TLS1.2. So I'm wondering that is that possible to use 512-bit or higher encryption on websites?
TLS does not support any cipher suite combination with a symmetric key size larger than 256 bits. Asymmetric key sizes are available up to 15360 bits, which correspond to a 256-bit symmetric security level.
RFC5246 lists the available cipher suite combinations for TLS 1.2
It should be noted that the symmetric security of TLS is not the weak point, and 128-bits should be more than secure enough for the next 30 years.
Not with the current TLS standard (v1.2), the strongest algorithm it appears to support is only Camellia or AES with 256 bit key lengths. The strength and type of the cipher actually used for a connection depends on the server's configuration and the client's browser. When browsing the internet it can be similar to a lottery regarding the quality and strength of the encryption you actually get on each site.