for 1: you are working with the grid tied inverter so the significant parameter is voltage, because you must maintain the voltage to synchronize the grid, so the modulation index related with magnitude give you the major controllability.

for 2: the dc voltage value is depends on type of inverter, is symmetric or asymmetric sources, individual or capacitor dc link and type of configuration, so based on your configuration it will be decided.

for 3: the control parameters are voltage variation on ac/dc side, limitation of harmonic content and type od control strategy.

for 4: over modulation give you the maximum utilization of fundamental voltage value. but the boundary is decided based on optimal position of required voltage and limits of harmonic distortions.

take modulation index -------unity .

Take DC link voltage 800V.

Value of inductor affects the modulation index.