>Is this poor throttle/clutch management on my part, or something to be expected?
In a word: yes.
In more words: Probably - You may need to check and adjust chain tension.
Also, as a newbie, you need to get used to small adjustments in steering, braking, clutch and throttle. It takes a while, but you'll get the hang of it.
It's more noticable in bikes like yours - 125s are light anyway, but the low-end torque of a Dragstar is comparatively hefty, even on the 125. The clutch is also a bit shite.
When you move up to a bigger bike, clutch-based manoeuvres will be so much easier!!
>to the point where if I want to pin it I have to adjust my grip forward to then pull >down further
Mine is a bit like that. Perhaps not so noticable, but very close.
Again, slight adjustment of the hand position, which will come to you. You can move your hand further round the grip either way, without actually altering the throttle position... That's fine control!!
Simple answer - Don't pin it. You will rarely need full throttle like that anyway, but you get better acceleration from a 125 Drag with a (relatively) gradual increase in throttle. Rather than shut to full in half a second, try working up to full over about 3 seconds. IIRC, you'll probably top out of your rev range before then and be changing up a gear anyway.
>will it damage my engine and should the problem be resolved by tightening the cables?
Eventually yes... and yes it will.
With properly adjusted cables, the throttle will spring shut when you let go (ie just loosen your grip).