What does "swooping out of the clear blue sky" mean ?
Since "swoop" means (here) "sweep through the air, as a bird or a bat" (from dictionary.reference.com), we conclude that the motion of the blue jay is to gracefully, gradually, following a smooth curve, fly [down].
The words "out of the clear blue sky" can mean "from nowhere in particular", although here they can mean literally, "from some distance/altitude at which the blue jay wasn't visible (due to haze or distance)".
So, to answer your second question
Does it mean "to float in the air" or "to descend to somewhere"?
yes, pretty much.
"Swooping out of sight
" also suggests gradual movement, smooth flight along a curved path, without sudden changes in direction or speed, then disappearing from the view.
"Swooping out of 1911 Baker Electric" means with a graceful, smooth motion, possibly with skirts in hand (reminiscent of a bird's wings), alighting from that vehicle.