After Login with Facebook,page loading for a long time

I'm not sure why it's going so slow. There are a couple of things that can cause it to go slow. They should all be easily fixable, but we'll need to narrow down the cause first. Can you try the following and let me know what happens:
* Do you have the same slowdown with Google+?
* Do you have any Social Profile plugins enabled? If you disable them, does the login process go fast?
* In the JFBConnect -> Configuration -> Facebook area, can you set the "Disable SSL Verification" to "Yes". Test if this speeds things up at all.
* In the JFBConnect -> Configuration area, set "Enable Debug Mode" to "Yes". Then, after logging in, there may be error messages displayed. If so, let me know what those are.

Let me know how the tests go, and we'll gladly help investigate further from there.

Thanks,
Alex

1.One the other problem is our site login with Google+ always show JLIB_ENVIRONMENT_SESSION_EXPIRED, and it still login success.

I've never heard of that issue before. Does it only happen with Google authentication? Looking through our code, if you see that error and it's thrown by JFBConnect, then authentication shouldn't work at all. My only guess is that you're see that error from another extension that is setting it during the login process.

Can you tell me the color of the background of the warning? Is it blue or red? That will actually narrow down whether its from JFBConnect or not.

2.When we login with google+ website always redirect to homepage not the original location. But FB login is work fine.

This is likely related to the issue above. When Joomla thinks the session has expired, it will always redirect the user to the home page.

Our site use JO social content locker plugin. The plugin conflict with Jfbconnect.
We make some modified.

No, you can't do that. The all.js file is the old Facebook Javascript library. It's not recommended to be used by Facebook anymore and JFBConnect expects the newer sdk.js file.

My recommendation is to remove the inclusion of the Facebook Javascript library from the other extension you're using.

I hope that helps,
Ale