Question

why the parameter hfe is implemented in h-parameter & why gm in hybrid pi model instead of hfe

Answer 1

h sub FE is the DC current gain, academically Beta sub 0
h sub fe is the signal gain, academically Beta
g sum m is the ratio of collector current to V sub T ~26 mV
h sub ie, ideal low frequency input resistance for common base, is Beta divided by g sub m.
Whether you use Beta or g sub m in your pi model depends on whether your using a current or voltage model.