apple pen 2nd Generation - tip wiggles

The metal transducer is a critical (and fragile) element of the Apple Pencil. It should not move in relation to the Pencil body.

As described, the tip of your Pencil has either been dropped onto its tip - or excessive lateral pressure has been applied. The Pencil is broken; the only remedy is replacement of the entire Pencil.

No.

If your Pencil is less than a year old, then it still warrantied and you can call your nearest, “local” for an appointment to get a free warranty replacement.

If the Pencil is over a year old, I am afraid you will have to purchase another new Pencil.

Apple Pencil are non-repairable.

Best of Luck to You!