chemical displacement

Definition of displacement in aqueous solution:
"Displacement is a reaction at which a more reactive metal displaces a less reactive metal from the solution of its salt."
For example, When a piece of copper (a more reactive metal) is put into silver nitrate solution (the solution of a salt of a less reactive metal), displace reaction occurs. In the displacement reaction, copper is changed (oxidized) to copper(II) nitrate solution and silver nitrate solution is changed (reduced) to silver metal, i.e.
Cu(s) + 2AgNO3 → Cu(NO3)2(aq) + 2Ag(s)
or: Cu(s) + 2Ag+(aq) → Cu2+(aq) + 2Ag(s)

In the passage, "coat" means "form a layer on the surface of". For example, "silver coats on copper" means "a layer of silver is formed on the surface of copper which has not yet been reacted". Note that before the end of the reaction, part of the more reactive metal is unreacted.

You have given 3 points of definition of displacement. The first point is part of the definition. The second and the third points are the description of the experiment. Actually, the second and the third points are incorrect. In the experiment, the less reactive metal formed is not a layer, but just some solid stuck on the surface of the more reactive metal. The solid is easily detached from the more reactive metal when the test tube is shaken. Therefore, if the more reactive metal is the limiting reactant, the reactive metal would be completely reacted (dissolved) at the end of the reaction.
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