How do you clean the wooden top safely?

Just dust it with a dry cloth. You can apply a thin coat of clear beeswax once or twice a year to feed the timber. Don't use spray polishes on the wood.

I have an old table that folds in half but the hinges are a bit stiff when you open it up, should I oil them?

A drop of light machine oil on the brass pin helps if the joint is sound. Wipe away any excess immediately so it doesn't soak into the surrounding mahogany. If the screws are pulling out of the wood, oil won't solve the problem. The holes need plugging with hardwood dowels before re-setting the hinges to take the strain off the joint.

What is a tilt top mechanism for?

Space was often tight in smaller rooms. The mechanism allowed servants to tip the large circular top upright and push the table flush against a wall. They pull out into the centre of the floor when guests arrive. The brass catch snaps shut to hold the top rigid while the cups are poured.

My table has a raised edge all the way around but there is a gap cut out on one side, what is this gap for?

That gap is left there by the maker so you can sweep crumbs off the surface. Without it, loose tea leaves and dust get trapped against the gallery edge. Antique tea tables with this specific cut-out serve a clear purpose. It shows a practical approach to housekeeping during a period when servants had to clear up quickly between courses.