Cool story, but there is no way we wouldn't have captured and analyzed the satellite by now. We do this with our own satellites, and would not think twice about capturing an unknown satellite.
Now, it is probably more likely that this is either one of our own secret satellites, or it belongs to Russia. We wouldn't touch a secret Russian satellite, as that could lead to war. I can see the gov sweeping that under the rug. There is also a lot of space debris floating up there, but anything with a signal can be tracked and captured.
a guy in the comments said the next to last pic is a surfing space cat.