Does the lack of receiver buffer space ever throttle the sender for these first four data$-$carrying segments?

No$.$ The receiver advertised window is always larger than the amount of buffering needed for more than twenty $1500$ byte segments.

Yes, the client refrains from sending the third segment, since there is not enough advertised buffer space at gaia.cs$.$umass.edu.

Yes, the client refrains from sending the fourth segment, since there is not enough advertised buffer space at gaia.cs$.$umass.edu.

I've got no idea $($note: this isn't the correct answer!$)$