I am a bit confused on how NHRA pro stock car's transmissions are working and was hoping someone could explain it.

Here's what I know:
they are 5 speed
they have a clutch pedal but only use it for launching after that every gear is shifted only by the cool lever

I'm assuming it's some kind of pseudo automatic but don't understand how the clutch pedal is only being used in one gear, also what kind of clutch are they using????

 

most race cars have a shift without lift (SWOL i think) system. on upshifts, its kinda like SMG. you keep your foot on the gas and just pull a lever to shift up. The car automatically releases/re-engage the clutch. They only use the clutch to launch and maybe downshift.

 

Since 1973, the most popular transmission was the Lenco planetary design, first used as a four-speed and now as a five-speed. Although still used in IHRA Pro Stock and in Air-Shifted three-speed units in IHRA Pro Modified, NHRA Pro Stocks utilize a Liberty or G-Force five-speed clutchless manual transmission.

 

so how does the clutch pedal fit in? Is it just build to engage in first and reversed?

 

Yes

 

you don't need your clutch to shift between gears in your car now. You only need it from adead stop.

I do it all the time......shifting at a leisurely pace without using the clutch. On our cars, you need to make your shift at the precise moment when the engine speed matches the transmission speed for your next gear (either upshifting or downshifting.) You can't do it for quick shifting in our cars, so don't try it!!!

On the racing manuals, they use special gearsets that allow for easy, full throttle, clutchless shifting. these are sometimes known as "crashboxes."