How to fix loose pivots?

Wooden threads strip over time. Adding a thin leather washer between the upright and the frame adds enough friction to hold the glass steady. For a loose metal screw, restorers sometimes pack the worn hole with hide glue and fine sawdust before re-threading.

Clean cloudy antique mirror glass?

You can't reverse mercury degradation. The cloudiness happens on the back of the plate where the silvering has oxidised, not on the front surface. Standard glass cleaners will only remove surface grease. Wipe the front gently with a damp cloth, but accept the grey spots as part of the age.

I found a mirror in my grandmothers attic and the base has three drawers but the middle one is locked and there is no key, can I open it?

A locksmith can easily pick a simple antique cabinet lock without damaging the wood. Most of these small drawer locks use a basic ward mechanism. You can sometimes source a generic antique key from a hardware dealer. Buy a bundle of small barrel keys and try them gently until one turns the lever. Never force the drawer open with a screwdriver. You'll split the mahogany veneer and ruin the drawer front.

The glass on mine is very heavy and thick with a wide bevel around the edge, does this mean it is a later Victorian piece or could it be earlier?

Early plate glass is heavy. Eighteenth-century glassmakers cast the plates and ground them flat by hand. Those irregular bevels often indicate early origins. Craftsmen ground the edges manually to fit the wooden rebate.