Converting PWM to bipolar square wave

On the bottom of page 350 of the microcontroller datasheet, it mentions that writing a small value to the timer value register during the overflow interrupt might cause the next interrupt to be triggered only on the next pwm iteration, since the timer continues to count while the interrupt routine is being executed.

An unsynchronized write to the TIM channel registers to change a pulse width value could cause incorrect operation for up to two PWM periods. For example, writing a new value before the counter reaches the old value but after the counter reaches the new value prevents any compare during that PWM period. Also, using a TIM overflow interrupt routine to write a new, smaller pulse width value may cause the compare to be missed. The TIM may pass the new value before it is written.

This is confirmed by the fact that the pwm value is held high for one entire pwm clock period + what looks like the timer length (based on the surrounding lengths). The value being written to the timer length register is probably close to 0 at the time of error, so it is quite viable that the counter has passed the smaller value during the interrupt, and would only trigger on the following cycle.

This could be fixed by increasing the sinusoid minimum level to a level higher than the time it takes to execute the ISR, or changing the mechanism by which the new level is set. The top of page 351 details how this may be done.

You understood right. The pins with the tilde (~) symbol are pins which are linked to an hardware PWM module (i.e. timer). Since it is a hardware module, it is independent of whatever your CPU does. As such, if you are stuck in a delay, your hardware PWM will still continue to generate the proper output signal. On the other hand, a software PWM (one that you would generate with a manual pin toggling) would be interrupted by your delay.

Most of the time, you should prefer hardware PWM over software PWM for many reason:

1. It's more reliable;
2. It consumes less power (you could sleep your MCU while still generating PWMs);
3. It allows you to do something else instead of servicing the switching;
4. It allows for larger frequencies, because you can typically get frequencies up to your MCU's operating frequency, while a software emulation involves a few operations, so you are not able to keep up;
5. It's more accurate: the hardware PWM is simply a divider on your MCU's operating frequency, while software PWM uses CPU instructions, which require branching. Since it is compiled code, it is more or less deterministic, so your duty cycle would not be exactly the one you expect (near, but not perfect nor stable if doing something else at the same time).