Well, the question says it all; is there a definition of body in physics? What is to be considered a physical object and what it cannot?
There is no general definition of a body for physics, as in everyday speech where one has to qualify further either by context or content.
A body of water, means a bulk ensemble of water molecules and further analysis depends on the context.
Two colliding bodies could be billiard balls or asteroids. It is a blanket term that needs further attributes if it is to be used in a problem that needs a mathematical solution in physics.
If you are talking about rigid bodies like billiard balls or asteroids one has a definition of a body:
However this seem a little bit fishy since it also uses the word “body” in its definition. However one can also define a body in Classical Mechanics as a collection of atoms (or just one atom for that matter) having a well-defined energy, velocity, mass and momentum. Things get a little complicated when you are dealing with QM.
To answer your second question: You can think of anything as physical object so long as you obey the above-mentioned rules. E.g. a body with infinite mass is not a physical object, it is just an idealisation of a very heavy physical object.