Sougatab,
I'm not sure what's causing the 404 on registration. The redirect on login (after the user is registered) is working fine. On registration, as you've noted, the page is always redirecting to:
component/jfbconnect/social-network-for-social-impact/profile
That's not being caused by JFBConnect. I notice you have some plugins like jomsocialredirect which can redirect the user after registration. I also noticed that the User - Contact Creator plugin was enabled. That plugin can cause a lot of errors if you're re-registering after deleting a user as the username will already be in the Contact database which throws an error.
I don't want to disable a lot of your plugins, but I think you need to disable a lot of plugins and just narrow down where the conflict is or what is really performing the redirect. You have 102 plugins enabled which is quite a few to diagnose and I don't want to mess too much with a live site.
You may also want to try a different template which is quick and may help expose the problem. Unfortunately though, we haven't heard of this issue on any other sites, so it makes it difficult to narrow down the exact cause. Hopefully disabling some other features will help narrow it down. If you do, let us know where the conflict seems to be and we should be able to help you work around it.
Thanks,
Alex