By default client cert option is select ignore in BIGIP. Like same We can need to do in server side (Because BIGIP is client for server when it is making a secure connection with bigip in offload time). am i right ?
yes
If Server is asking for client auth while making a connection from BIGIP to server side when Cert bigip will present to server.....Is it self sign cert ?
server is the one who verifies certificate bigip (serverssl) provides. if server accepts self-signed certificate, yes you can use self-signed certificate in serverssl profile.