Bouncing radio signals off of LEO satellite repeaters like the ISS is surprisingly easy. All you need is a couple of inexpensive handheld transceivers, an antenna (that you can build) and an amateur radio license.
I have the stuff in your video but no idea what you're doing. Can you explain some more? I assume the ISS transmits some image data modulated as audio, which the computer can then read via the Baofeng and convert back to an image?
Quansheng* radios, headphone and mic jack adapters for the radio and your phone, and software to decode ham digital modes.
As far as the license goes, arrl online will have resources for your area to take the required test.
* Yes I know most people think of baofeng but after owning lots of cheap radios the best, far and away, is the quansheng. They're very loud and clear with receive audio, they are yaesu accessory compatible (iirc) and the older ones are basically the Nokia handset of handheld radios.
This is really neat, glad it made it to the front page! An interesting next step could be: do it with a budget of less than $x, gradually decreasing x each time.