I drive a '97 FD and drive it sparingly around once every 2 weeks. I started the car up, shifted into 1st gear as usual and tried to get the car moving with the clutch but it refused to move even at the friction point. After putting in some gas, a loud thud comes from the rear of the car, and it lunges forward very slightly and suddenly starts to move as usual.

The issue happened to me repeatedly for around 4 times, and it only happens for the first time that I take the car out of the garage after startup. Also, I always made sure that the handbrake is properly disengaged (The handbrake is very loose anyway, it doesn't have enough stopping power to hold the car in a slope either.)

 

This sounds like one or both rear brake calipers sticking or not releasing properly. Have you tried jacking the rear up and turning the rear wheels by hand BEFORE driving the car? One of the most common causes of sticking calipers is that the sliding surfaces aren't letting the caliper and pads move due to lack of lubrication, rust, etc.

This thread is about the FC, but the FD is the same idea (single piston rear caliper).
https://www.rx7club.com/2nd-generati...-pads-1122303/

Specifically, look at the 2nd picture, also linked here. See how the pad fits inside the metal anti-rattle clips? It has to be able to move freely along there when the piston moves.
https://www.rx7club.com/attachments/...s-img_2525.jpg

As for the other pad (not pictured), the entire caliper moves on the Slide Pins so the pad can meet with the rotor when you step on the Brake pedal. The Slide Pins inside the black rubber boots can be seen here (same thread as above)
https://www.rx7club.com/attachments/...s-img_2524.jpg

If one or more of these sliding surfaces are sticking, the caliper can't release correctly.