1) Consider liquid water in contact with a gaseous mixture of air and water
vapour. Water evaporates when the vapour pressure of the liquid water
is greater than the partial pressure of water vapour in the gas; i.e.
when the rate at which molecules leaving the liquid is greater than the
rate at which they are entering the liquid from the gas. Water will
evaporate only until there is a state of (dynamic) equilibrium between
the liquid and the vapour.
2) In general, molecules of water near the liquid-gas boundary may escape
from the liquid provided they have a small energy necessary to overcome
any surface forces. Molecules with a whole range of kinetic energy can
leave the liquid, not just those with extremely high energies.
(Incidentally, what do you mean by kinetic energy higher than the boiling
point?)
3) Freezing is a collective event. A single molecule cannot "freeze". At any
given instant, there may be many molecules with small or even zero
kinetic energy but these will be jostled by their more energetic
neighbours within a very short time, so there is no local freezing
possible at temperatures above the freezing point.