If you're using mac version LW & select the direct connect search it will show you. Apparently on the windows version it doesn't. But you can find out here: http://www.whatismyip.com/

About Browse, search the word browse on the forum. I've posted some recent answers about this. It helps if you the other person has chat enabled, particularly for those uploading from you. But still no guarantees.
You can also try Direct Connecting with them. You can search direct on the forum also.