1. Don't use the compat version of jQuery then if you don't need to support old browsers. jQuery 2 exists for a reason.
2. Yes, JSONP is a way to transport data between different domains. Don't call domains you don't absolutely trust. JSONP isn't a fault of jQuery, but the browser security model.
3. jQueryUI is a different dependency. Don't use it if you don't want it. It really depends on your application though, if it's presenting a UI, then are you going to implement it all yourself, or pick one of the many UI JS libraries that will be in the same size ballpark. Browser downloads once, browser caches, job done - and these libraries are usually accessed from a CDN, so you probably already have it in your cache.