If the input impedance is not infinity then the input voltage will be decreased by a factor before getting amplified.
If the input offset voltage is non-zero, then the input-output characteristics curve will also be offsetted.
I don’t know about frequency response.
Note: It may save the power of the power source and provide the current flow higher than the support of the power source.
(4) & (5)
Skip and check later. Too many new stuffs. Possibly relevant.