1) Is HTTP Basic Authentication useful/fast in case of thousands and thousands of client requests per second?
Basic Authentictaion is quite simple, so it doesn't take a lot of processing. Thousands of requests per second of course requires serious hardware, certainly several load-balanced servers.
2) Is there any other mechanism to deal with high volume requests? How about the cases where the client requests without user credentials still need to be processed and thus pass the security mechanism?
I'm not sure what you're asking. If a request comes in that doesn't need to have authentication applied, then don't check for it.
3) Also is http basic authentication be used with weblogic server?
Basic Auth is part of HTTP, and thus supported by all compliant servers.