At bar 3 to 4 the "Em7-5" goes to "Dm/F" could this be consider as a half step chord movement ? because the inversion bass F ? even tough "Em7-5" and the actual chord "Dm" without the inversion is not a half step related ?
The use of Dmin/F (F in the bass) creates a smooth linear movement of that voice. This does not make the progression chromatic. It will still have the feeling of resolution to Dmin, rather than E-->F using bar chords or some similar device. It is not uncommon in harmony to arrange the chords (i.e. voices that support the melody) in such a way that each voice has its own melodic structure. I agree with Michael Curtis' last statement
"It would help to know what happens in bar 5 to know if one or the other interpretation of the chord in bar 4 makes sense."