Yes gravity very probably does propagate at the speed of light. If it were
instantaneous a lot af problems would occur with causality ie. the cause
of an event must occur before the event itself. One point of view is that
it might be propagated by 'particles' called gravitons however there is,
at the moment, no evidence for this.
The reason a black hole can prevent light escaping is because the field is
already there and so can act on the photons. You could think of the black
hole as a 'source' of gravitons streaming out all the time, consequently
if the black hole is 100 years old its gravitational well will be 100 ltyrs
radius (discounting the gravity of the star that was there previously).
Finally, no, you have not made a perpetual motion machine using gravity
waves and a black globe. All you have is a machine for extracting energy
from gravity waves, much like wave-powered electricity generating schemes
which turn water waves into electricity - these aren't perpetual motion
machines!
Roger