The person who makes the furniture is called a wood smith, as for the person who sells the furniture, I don't think there is a specific word for it.
a person who makes furniture
A Carpenter or Woodworker, and sometimes, Cabinetmaker.
Cabinetmaker
A thin covering on wood is veneer.
Teak furniture is a high quality wood furniture. It is made from a tropical wood, teak, that is extremely durable, dense and weather resistant. Teak furniture is often used as outdoor furniture.
A woodworker, a carpenter, furniture maker, wood carver.
Sheesham Wood is a type of wood originating from renewable, sustainable sources. Because it is a type of wood for furniture, and not a style of furniture, Sheesham Wood furniture can be located anywhere wood furniture is sold.
A carpenter. If you want a more specific term you could use Lomwright for men and Lomwrit for women. The art itself is Lomary from the Anglo-saxon Lóma meaning household furniture
reclaimed wood or salvaged
butts factory
This is called "marquetry".