STM32: Running many peripherals at the same time
You don't need to exercise every peripheral, only those you use in your product. STM32 has clock gating and nearly all optional peripherals are disabled at startup. You only need to be concerned about peripherals that you enable in your production firmware.

As far as simultaneous operation is concerned, if you actually need that (it seems a different mode of operation from your production code which you say is blocking, so EMI may be different, too), you have 3 options: interrupts, DMA and preemptive RTOS tasks. Each of these is a topic in itself, but many examples exist, e.g. most examples that come with the standard peripheral library are interrupt-driven. Note that small implementation details may again result in very different performance (and therefore bus and peripheral activity). Making "all peripherals churn full-speed at the same time" is a very challenging task if you actually mean that literally.