Antiphase PWM per motor looks OK.
Disabling IC using EN lines will often create large motor spike - as long as internal IC catch diode rating is OK that's OK. Otherwise add external diodes to supplies.
What battery chemistry. What size?
AA Alkaline will often tolerate significant regeneration.
Unless battery is small physically or you want exceptional shelf life then NimH will be better than Alkaline. For very long shelf life LSD NimH are getting very good.
At AA size, energy density of NimH now equals or exceeds Alkaline and high load dishcharge characteristics are much superior so there is little reason for Alkaline.
At small cell size Alkaline MAY make sense.
I have not tried this
Answer is "seems like this to me".
Caveat emptor :-):
Motor inductance and resistance will set t = L/R time constant. But, very easy to put small resistor from motor to ground, apply voltage and watch voltage in resistor and thus current rise on scope. PWM period which is small compared to total motor rise time will (probably) be good.
I'm not sure why you think BJTs are significantly slower than power MOSFETs; that's certainly not an inherent characteristic. But there's nothing wrong with using FETs if that's what you prefer.
And MOSFET gates do indeed need significant amounts of current, especially if you want to switch them quickly, to charge and discharge the gate capacitance — sometimes up to a few amps! Your 10K gate resistors are going to significantly slow down your transitions. Normally, you'd use resistors of just 100Ω or so in series with the gates, for stability.
If you really want fast switching, you should use special-purpose gate-driver ICs between the PWM output of the MCU and the power MOSFETs. For example, International Rectifier has a wide range of driver chips, and there are versions that handle the details of the high-side drive for the P-channel FETs for you.
How fast do you want the FETs to switch? Each time one switches on or off, it's going to dissipate a pulse of energy during the transition, and the shorter you can make this, the better. This pulse, multiplied by the PWM cycle frequency, is one component of the average power the FET needs to dissipate — often the dominant component. Other components include the on-state power (ID2 × RDS(ON) multiplied by the PWM duty cycle) and any energy dumped into the body diode in the off state.
One simple way to model the switching losses is to assume that the instantaneous power is roughly a triangular waveform whose peak is (VCC/2)×(ID/2) and whose base is equal to the transition time TRISE or TFALL. The area of these two triangles is the total switching energy dissipated during each full PWM cycle: (TRISE + TFALL) × VCC × ID / 8. Multiply this by the PWM cycle frequency to get the average switching-loss power.
The main thing that dominates the rise and fall times is how fast you can move the gate charge on and off the gate of the MOSFET. A typical medium-size MOSFET might have a total gate charge on the order of 50-100 nC. If you want to move that charge in, say, 1 µs, you need a gate driver capable of at least 50-100 mA. If you want it to switch twice as fast, you need twice the current.
If we plug in all the numbers for your design, we get: 12V × 3A
× 2µs / 8 × 32kHz = 0.288 W (per MOSFET). If we assume RDS(ON) of 20mΩ and a duty cycle of 50%, then the I2R losses will be 3A2 × 0.02Ω × 0.5 = 90 mW (again, per MOSFET). Together, the two active FETs at any given moment are going to be dissipating about 2/3 watt of power because of the switching.
Ultimately, it's a tradeoff between how efficient you want the circuit to be and how much effort you want to put into optimizing it.
The FET controls the motor. The diode is not part of the control as such. The diode is there to kill off any voltage spikes that occur when the FET opens and the motor is turned off. The diode will only be forward biased when the motor shuts off (the FET opens.) The coils in the motor can generate a pulse higher than the supply voltage. The diode would short out any such pulse and prevent it killing other parts of the circuit.
The capacitor is there to filter out the RF garbage that the motor puts out - the sparking you can see on a DC motor causes RF interference. The capacitor absorbs that and makes the motor much quieter (RF wise, at least.)
I would assume that Rx is planned for use when a different opto-isolator is used - an isolator in which (for what ever reason) the base of the BJT floats up and could cause spurious operation of the motor.