How do I get the current user’s info over Ajax?
For the redirect I agree, I could not get it too from ajax response, so I just saved it before the ajax call.
var returnUrl = $("input[name='redirect']").val();

Then I can make the redirection :  

.success(function(data) {
    if (data.success) {
        window.location.href = returnUrl;
    }


For the user's data could you precise what you want to do?