As an aside, isn’t Satan going to be cast into the Lake of Fire also? I realize he isn’t physical (at least not in this dimension).
Oh yes; clearly stated in the above passages.
He’s chained in the bottomless pit (interesting) during Christ’s Millennial Reign - let loose once again for a short time then will be there with the Beast and the False Prophet in the Lake of Fire at the end of the 1,000 years.