Redshift/Blueshift of Gravity Waves Around a Black Hole

nottay

First time poster and curious about how the shifting of gravity waves affects the curvature of space-time for observers in the vicinity of a black hole's event horizon. I'm making some assumptions based on my own research on the topic.

Assumptions:
1. Gravity waves are traveling distortions in space-time curvature traveling at the speed of light due to the changing motion of masses rotating about each other.

2. Gravity waves can be redshifted/blueshifted depending on the relative motion of the observer to the emitter and by gravitational field differences between the observer and emitter.

3. To an observer above a black hole's event horizon all EM and gravity waves emitted radially out at the event horizon and within it are infinitely red-shifted to an infinite wavelength.

Questions:
1. Would an observer at a black hole's event horizon see incoming gravity waves gravitationally blue-shifted to such a high frequency that space-time would appear crunched into a tighter density?

2. If gravity waves of high frequency trying to escape an event-horizon are red-shifted to a frequency of zero for an outside observer, is the opposite true that flat space-time would appear blue-shifted to a gravity wave of high frequency for an observer at a black hole's event horizon?

Thanks for any help on this issue you can offer!