LimeWire is the name of a popular P2P program.
P2P stands for "Peer to Peer". You are correct to assume that when you download a file on a P2P network, you also upload that file to other people who would like to download it as well. In turn, other people must upload the file to you for you to download it. This is how a Peer to Peer network works. If no one uploads anything, you wouldn't be able to download anything.
Yes. If someone downloads from you, it does count towards your monthly data usage.