How do I clean the inside of the pot?

Silver pots just need warm water and mild dish soap. Use a soft cloth to reach inside. Rinse well and dry straight away. Leaving water inside causes tarnishing over time. Ceramic sets can take a gentle soak. Stubborn stains usually lift with a weak solution of bicarbonate of soda.

We inherited a big silver plated coffee service from my grandmother and one of the small wooden handles feels quite loose when you pour, can this be fixed?

A silversmith can tighten a loose handle quite easily. They usually tap the original silver retaining pins deeper into the wood, or replace them if the wood has shrunk too much. It is a routine repair. Do not try to glue it. Glue rarely holds against the heat of the liquid and it makes the silversmith's job much harder when you eventually take it in.

Can you still use them for hot coffee?

Yes, most sets are entirely functional today. You should warm the pot with hot tap water before pouring boiling coffee in. This prevents thermal shock in ceramics and reduces stress on the metal joints.

I read somewhere that old silver teapots and coffee pots have ivory insulators to stop the handles getting hot, how do I know if mine has them?

Look at the small spacers where the handle joins the pot body. Silver handles often feature thin discs inserted to break the heat transfer. If they are white or cream with a subtle cross-hatched grain, they might be ivory. Many makers used bone or wood instead. Bone tends to have tiny dark pits on the surface. If you are unsure, a dealer can check the grain under a loupe.