Sticky throttle cabel

Possible shifter fork in the tranny is broken. Also inside the engine there is a little lever that pulls on a pin when shifting. That pin could be broken. Also pull in the clutch lever and try to push the bike if it moves then the clutches aren't stuck together if it doesn't move freely then its possibly a set of stuck clutch plates. That's a simple fix.

Loosen the handle bar adjustment a lot, .then take a little slack out of the cable at the engine connection, then re-adjust the handlebar lever with a bout 1/8" play

make sure your cables are not binding up somewhere. sounds like the throttle is sticking open. nothing to do with the trans.

This can happen if you used the wrong oil. Is the clutch cable or hydraulic operation. If cable then it may be dry or adjusted too much (needs a little free play at the lever. Not sure of your knowledge so starting with the basics. How many Kms has it done.

The one way clutch that engages the starter motor to the flywheel is chattered or damaged and needs to be replaced. The starter motor turns a small gear that is connected to a large gear by a small chain. On the side of the big gear is a smooth machined surface that the one way clutch grabs when the starter is engaged. The surface is chattered and the three grabber rollers wont jam or grab on the surface unless it is smooth therefore the starter spins but the motor does not. You will probably have to replace the large gear and possibly the three rollers also.

I want to know- if there is a big difference between a 2001 v-star classic and , say a 2005 or 06 v star classic. Are the newer ones lighter, or advanced in some way, enough to make a difference?

May be possible that clutch is disengaging when shifting to first and/or drive not fully switched into first gear. Your 1st gear light may be lit, but actually isnt in a ready state.