faint, feint, and feign all come from the French, feindre, which is derived from the Latin, fingo, shape. The first two, similarly pronounced, have very different significations. Faint means a sudden loss of consciousness or swoon; feint signifies a deceptive move or pretense. To feign is to make a false show of; pretend.
fake: Slang term for imposition; fraud; also, fictitious or manufactured news. Expressive but inelegant.
fakement: Slang for an act of fraud. Less desirable than preceding and equally inelegant.
fanatic. Compare enthusiast.
farewell: When separated by a pronoun farewell is written as two words; as, fare you well. Exception has been taken to Byron's pathetic lines
Fare thee well, and if for ever,
but this is hypercriticism for here the pronoun is nothing but the Anglo-Saxon dative.
farther, further: Farther should be used to designate longitudinal distance; further to signify quantity or degree. Thus, "How much farther have we to go?" "Proceed no further along that course."