if anyone can tell me if Arduino is fast and capable enough to capture without loss data coming from a USB 2.0 device, send it streaming to the Internet, and at the other end to have another Arduino device that reads from the Internet (having set up IP handshakes, of course) and recreates the data to an output USB 2.0 port.
Simple answer: No. None of the available Arduino models is fast enough for such a job. If I understand your idea correctly it isn't even possible to do it because USB won't work that way.