Current EGit version (3.3) is secure to clone and authenticate users over SSL?
I have been reading about 1024-bit SSL is not used anymore, so what SSL version uses EGit?
and how about HTTPS?
EGit is only a client. The server determines which connections are possible to connect with and how strong the key used in the certificate is. So there is nothing EGit can reasonably do wrong in the direction you are asking. You need to read up on SSL/TLS to get a better grasp on which security aspects to look for.
HTTPS is HTTP over SSL/TLS so the question is the same as the first.
There is no such thing as '1024-bit SSL'. There are SSL certificates based on 1024-bit key pairs. It is those that most certificate signers will no longer accept. This has nothing to do with SSL versions, or implementation versions either.