Question

What happen to the electric field inside the metal conductor?

How is the electric field affected by the presence of the floating conductor?

Answer 1

1)
Electric field inside the metal conductor is zero.
If the electrons within a conductor have assumed an equilibrium state,
then the net force upon those electrons is zero. The electric field
lines either begin or end upon a charge and in the case of a
conductor, the charge exists solely upon its outer surface. Thus the
field inside is zero.
2)
Electric field lines will enter and exit the conductor; the conductor
will be surrounded by and will not intersect any equipotential lines.