You don't need any special equipment. A baofeng or RTL-SDR will work fine. The stock antenna on a baofeng will pick up the ISS on a high elevation pass if you hold it sideways. A handheld yagi can be built from some scraps of wire and wood.

No, you need an audio interface such as a Signalink or Digirig.

You could also make a simple interface with a couple of audio cables connected to your sound card. You will need an L pad to reduce the line level from the computer down to microphone level for the radio. For some modes like SSTV, you can use the VOX function on your radio to transmit, Many other modes will need some sort of PTT control because VOX will be too slow.

Yes, you can use a vertical antenna, but it's not ideal. There is a null overhead. They will work better on lower elevation passes. If the vertical is on an HT, you can hold it sideways to receive on a high elevation pass.

There are omnidirectional antennas for satellites such as a quadrifilar helix or turnstile antenna that will work very well for stronger signals like the ISS and the old NOAA satellites.

I wouldn't go any closer than 2 wavelengths. 3 or more would be preferable.

Keep the transmitting and receiving antennas a few wavelengths apart to prevent damage, farther if you're using an amplifier. You can transmit right next to the RTL-SDR with an HT if you disconnect the antenna from the SDR. It will still receive the signal from across the room.

The ISS is an easy one to start with. The signal is much stronger than most of the others.

PVC doesn't really work well for a mast above 20 feet or so. Pipe couplers are not strong enough to join the sections, there needs to be a foot or more of overlap.

Sdrplay does work on Linux. Unfortunately, the driver is closed source though. You will have to install it manually and possibly have to compile the software you use to enable that driver. Also, the driver is only available for X86_64 and ARM64, so if you are using any other CPU, then it won't work.

I have an SDRplay RSP1A and it works best using SDR++. GQRX works, but there is no low IF mode and no control over the filters or bias-t. CubicSDR and SDRangel work too, but low IF mode is buggy. The hardware is good, but I never would have bought it had I known the driver was closed source.

There is also the QMX transceiver from QRP Labs. It can do CW as well as single carrier FSK digital modes.

I would suggest getting a radio that can do SSB. There are a lot of digital modes that won't work with radios like the QDX or QMX.

You can run a dipole between two houses, just be sure to do your RF exposure calculations and don't be surprised if you pick up a lot of RFI. You will need to use insulators between the antenna wire and the supporting rope. There is a lot of voltage on the ends of the dipole. If the dipole is less than 1/4 wavelength off the ground, most of the signal will go up. That's good for NVIS on the lower bands, but bad for DX.

You can put multiple dipoles on the same cable, it's called a fan dipole. The wires have to be spread out and can be a pain to work with, but you can get an antenna that's resonant on multiple bands.

Most radios won't run on 20V or higher. At 15V or lower, USB PD is limited to 3A.

If you wanted to get 100 watts, you would need a buck converter to step 20V down to 13.8V. Now you have two switch mode power supplies producing RFI.

How much RFI do those power banks spew out?

USB PD only goes up to 3A at 15V. That's not enough current to run a mobile radio.
A small LiFePO4 battery is a much better choice as it will supply a stable 12.8V without any switch mode supplies.

SDR++ seems to work the best with my RSP1A, I still have to use a closed source driver that hasn't been updated since Dec 2019. At least the driver works fairly well, but sometimes it locks up and the sdrplay service has to be restarted.

The Android driver, on the other hand, is completely broken. It usually crashes within 5 minutes and it only supports up to 2msps. They haven't updated it since Feb 2019.

It works, but it's closed source and pretty basic. I just wish they would release an open source driver.

You could try some Motorola DTR or DRL radios if you want something license free and not super expensive. Motorola claims they cover 300,000 sq ft indoors. They put out 1W on 915MHz, they use frequency hopping spread spectrum, and they have digital audio.