The only proper factor of four is two.
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It depends on the number being factored. 22 is a proper factor of 44. 22 is a factor, but not a proper factor, of 22.
No, prime numbers do not have proper factors.
In the context of primes and factoriation, every counting number is a factor.
4 3 and 6 have no proper factor in common. Remember that 1 is a factor of every counting number, but not a proper factor of any of them. Greatest common factor questions do not recognise 1 as a proper factor. When talking of primes neither 1 nor the number itself is regarded as a proper factor.
Every number has one as a factor because one can divide into any number with no remainder. Every number does not have one as a proper factor because the set of proper factors does not contain one and the number itself.