Can a Skyline GTR have a clutch and be automatic?

Answer 1

No.

For a start, the Skyline GTR comes with a manual gearbox - 5 speed in the case of the R32 and R33, and 6 speed in the R34.

The reason the answer is no is that with a manual gearbox the engine (essentially the crankshaft) is connected to the gearbox via the clutch, where the clutch is (for the sake of argument) two plates that rub together becoming fully locked when the pedal is all the way out and not touching each other/totally separated when the pedal is all the way in. With an automatic gearbox - that is, a true automatic gearbox - the engine is connected to the gearbox by a torque converter INSTEAD OF a clutch. The torque converter is basically a vat of viscous fluid connected to the gearbox with a fan/propeller like implements inside it - engine spins and transfers rotational motion to the gearbox by the propeller spinning in the fluid. (this explanation has been somewhat simplified here).

Now, where things get a bit weird is where manufacturers start talking about "semi auto/tiptronic" boxes or "sequential manual" boxes. Without going into two much detail, there are broadly two types. Semi autos are often just automatic gearboxes with a manual override (still a torque converter but you can put the box into manual mode where you select the gear). These are generally very smooth like true auto boxes. Sequential manuals are a manual gearbox with two solenoids to control shifting and one to control clutch (they are a real manual gearbox, so do have a clutch). Many of these have an automatic mode, but are not as smooth as auto boxes when in that auto mode. Neither of these types of boxes generally have a "clutch pedal" - the auto box based one doesn't have a clutch and with the manual box based one, the gearbox automatically disengages the clutch when you come to a stop to prevent stalling.

The Skyline has neither of these (only a true manual gearbox with a stick and a clutch pedal).

Hope that helps.