OSQZSS

You need attenuation, not gain.

What is your target device?

The satellite motion creates a small frequency shift due to the Doppler effect.

Yes.

Since the time stamp of the sampling data is the signal "reception" time, you always receive "delayed" navigation data. At the simulation time of the beginning of the first subframe,...

For TX, higher bandwidth requires higher sampling rate and more computational power.

https://www.ngs.noaa.gov/CORS/RINEX-2.txt

https://gage.upc.edu/gFD/

Check NAV-CLOCK message. You can find the total frequency offset caused by both the receiver and transmitter clocks. This should be typically less than a few ppm.

The unit of the speed over ground in the RMC message is knot.