A tile installer or tile setter.
Assembly would be a name for putting things together.
The person is a steel-worker.
it will heat as long as the gas is on and your pilot is still lit, you would have to call your gas company to turn it off.
hydrologist
an inventor
Tiles are the "square things". Altogether, the tiles make up the floor.
A tile installer or tile setter.
A bricklayer or bricky
That person is a litter-lout, who is littering by dropping rubbish on the floor.
A picture made with with tiles and stone is a mosaic.
"Cuts up" is an unnecessarily crude way of putting it, but such a person is called a pathologist.
In the UK we call it the ground floor.
In America, a flat is an apartment. You might call that person an apartment dweller, a tenant, a renter, or in the case of a coop, they would be called the owner.
Google "replacement floor tiles". Example of what may be found: www.stonelocator.com. or google "floor tile replacements" Examples found: http://www.thisoldhouse.com/toh/skill-builder/0,,20057064,00.html
They call the tiles "bones." The pile of shuffled tiles is the "boneyard."
Catching tiles
Call a terrazzo floor installer.