Is it a common airline practice to base T/O speeds on the actual T/O weight when an assumed temp thrust is used?
You determine the t/o thrust as a function of t/o weight and runway length
Once the t/o thrust is determined you can select the assumed temperature on the thrust limit page on the CDU.

V1 is not the target primary parameter, it is a consequence of the calculation, on modern FMS your calculated value is cross checked with a range calculated by the FMS, that is your calculation could be rejected by the installed FMS unless you may force your value on some models.

A minimum rate of climb is necessary with a speed of V2+10, and at worst V2 with engine failure.

Backward of this Vr is computed.