Starting torque of series vs shunt DC motors
while in DC shunt motor torque is proportional to field and armature current but in this case value of field current is very less ( because we take resistance of field winding very high )

Not quite -- a typical shunt-wound motor has more turns of wire in the field to go with that higher resistance.  Since the field is proportional to turns * current, and smaller wire is both higher resistance and smaller, it's easy to wind the coil such that for the same amount of power dissipated, the generated field is the same.

1.Why we keep high resistance of field winding in shunt DC motor , isn't low resistance of field winding in shunt DC motor can provide same benefits as of series like high starting torque ?

Power dissipation and convenience.  In a series-wound motor you want most of the voltage available to the armature -- so you wind the field with a short length of thick wire.
For series-wound motors that are starting up, the start-up event is -- hopefully -- not going to be happening for long.  So you can dissipate more -- potentially lots more -- power in the field coil during start than you could continually.

2.Why we don't consider Inductances of field winding for starting torque calculation (While I think Inductance value must be high as it is wrapped on a ferromagnetic material) for starting torque calculation ?

Because the electrical time constant of the coils is very much shorter than the amount of time it'll take the motor to spin up.  So it can generally be ignored.

And isn't starting torque should be zero​ in case of series and shunt motor as Inductances of field winding doesn't allow current and hence starting torque is zero?

Technically yes, but again, the time L/R time constant of the coils is very much lower than any mechanical time constants, so you can almost always ignore the electrical dynamics.