How to stick a plastic clock hand to a metal spindle

In the strictest sense, if it has a metallic finish, it is metal, though it may only be a few molecules thick over a plastic substrate. But you refer to the base material. It can be hard to tell when it's in place due to the resistance of the mechanism masking the apparent mass. The way to distinguish without destructive sampling is essentially it's mass. Metal is denser than plastic. Removing the handle will usually make it easy to to tell just by weight. Many modern faucets are often made of both metal and plastic parts though.

One can still be fooled by weight. A solid, quality plastic handle may weigh more than a hollow, thin, cheap brass handle. The only sure way is to take a sample by drilling a small hole in an inconspicuous place. The shavings could be tested in a lab, after which they could determine exactly the type of resin or metal composition, if you paid them enough.

It usually suffices to simply hold a flame to the shavings. Plastic burns, metal does not.

I have had success sawing through them with dental floss. Get an 18" piece of floss. wrap each end around your fingers or a pencil. Slide the floss behind the plastic section. while applying a downward pressure on the floss, move it back and forth left to right until the hook separates from the adhesive. Once you have access to the adhesive you can scrape it off or use an adhesive remover like GooGone, rubbing alcohol or citrus based cleaner.