JSONP Support

Yes, it does. Moreover, JSONP is just a communication technique used in javascript, not a standalone language.

Yes it does.

You can also raise a support ticket to ask Lithium to allow cross site requests, avoiding the need for JSONP - you'll need to specify the domain/domains your JavaScript will be hosted on.

Yes shridharmishra , as nathan  mentioned, you can get the Endpoints enabled for your community as well and then use it without having to encounter any cross domain issues by whitelisting your other domain in lithium.

I want to follow up on this thread. The official recommendation from Lithium is to use CORS, not JSONP. We will continue to support customers currently using JSONP, but we cannot guarantee continued support in future releases.