How do you clean a mahogany pot cupboard?

Dust the surfaces with a soft dry cloth. Avoid spray polishes because they build up a sticky residue over time. Feed the timber once a year with a good quality beeswax. Apply it sparingly with a soft rag, leave it for twenty minutes, and buff it back to a shine.

I picked up a small bedside cabinet with a handle cut into the top but the door seems stuck fast, any ideas why?

Wood moves across the seasons. High humidity often causes a solid timber door to swell and bind against its frame. This happens often if the cabinet spent time in a damp outbuilding before you bought it. Move the piece into a dry room and wait a few weeks. Check the hinges if the door still catches. Worn brass hinge pins can cause the door to drop slightly and drag on the bottom edge.

What exactly is a tambour front?

It is a flexible wooden screen made of narrow strips glued to a heavy cloth backing. The screen slides along a curved track cut into the carcase. Cabinetmakers used them to save space in tight bedrooms. A sliding tambour requires no clearance to swing open.

There is a circular hole cut right through the middle of the shelf inside my pot cupboard, was something supposed to go in there?

Yes, that circular cut-out was designed to hold a specific wash basin or chamber pot securely in place. The rim of the ceramic vessel rested on the shelf edge, stopping it from tipping when the cupboard was moved. Many antique pot cupboards have lost their original fittings. Dealers sometimes fill the hole with a replacement piece of timber to make the shelf flat and usable for modern storage.