Bike creeps forward in first gear even with the clutch lever pulled all the way in — how worried should I be?

The warm-makes-it-worse detail is a genuine clue, and it points at the oil rather than the mechanism.

Oil thins as it heats. Thinner oil between the plates should mean less drag, so if drag increases when warm, something else is changing — and the usual candidate is the plates themselves. Friction material swells slightly with heat, and plates that are near the limit for warp or wear will close that fraction of a millimetre once they expand.

It also fits an oil that is not rated for wet clutches: those additives do their work more effectively at temperature, which is exactly when you notice it.

So: check the oil specification, and if it is correct, the plate stack is the next place to look.

This is clutch drag, and in the common cases it is an adjustment or oil problem rather than a failing clutch.

A wet clutch — which nearly all motorcycles have — is a stack of friction plates and steel plates sitting in engine oil. Pulling the lever separates them by a fraction of a millimetre. It does not create a vacuum between them: the oil film still connects the two stacks slightly, and a small amount of torque always crosses. A little creep at a standstill in gear is normal on many bikes.

What makes it excessive is usually one of:

• Too much free play at the lever, so full travel is not fully separating the plates
• Warped or sticking plates, often from age or from sitting unused
• The wrong oil — anything with friction-modifying additives makes the plates slip past each other rather than releasing cleanly

That last one is worth checking first because it is the cheapest and the most common self-inflicted cause.

For question 3, the practical line I would draw:

Ride and monitor if it only creeps at a standstill, gear changes are clean, it does not slip under acceleration, and you can find neutral with the engine running.

Stop and fix if any of these appear: you cannot find neutral at a standstill, changes start crunching, or the clutch slips — revs rise without the bike accelerating. That last one is the opposite fault and it is the serious one, because a slipping clutch destroys itself quickly and can do it mid-overtake.

Also adjust the lever free play before anything else. It is a five-minute job with the cable adjuster, it is the most common cause, and doing it first means you learn whether the rest of the diagnosis is even needed.