A circuit question using multiple MOSFETs with PWM control
1-) Is it fine as in my diagram to connect all the gates at a point and trigger four MOSFETs from a single input?


Technically yes you can wire MOSFETS in parallel like that and they will work. However, you need to remember that the gate of a mosfet is effectively a capacitor. As such, four in parallel is four times the capacitance. That means the switching time of the four gates will be roughly four times slower than using a single device.


  2-) Are the gate resistors values for R_g1, Rx_1, R_g2, Rx_2 correct/sufficient?


They look fine, and typical, to me.


  3-) It seems I wouldn't need heat sink by looking at average power dissipation. But I wonder if I should change the PWM frequancy. Currently it is 490Hz. Would it make sense to increase it to 30KHz for instance to prevent ringing sound or another issue?


Higher PWM, assuming you can switch the MOSFETS that fast, will cause more heating losses in the MOSFETS and reduce the efficiency of the circuit. At some frequency point you will need a heat sink. It will however reduce the audible effects. There is a compromise in there somewhere that you need to figure out. Either way you need a frequency high enough so that the ripple on the current through the inductors is fairly small.