Electronic – High resolution timer on the BeagleBone

The processor on the BeagleBone is not a microcontroller, but rather a microprocessor (the Sitara AM3359 from Texas Instruments), which doesn't have non-volatile memory on the processor itself, but rather tries to load programs (such as an OS) into RAM via a communications interface (UART, USB, Ethernet) or from an external memory (FLash or memory card). The initialization/booting process for this processor is described in detail starting at page 4667 of the technical reference manual.

It seems the latter (booting from a memory device) is the case for the BeagleBone, which means you can "program" the BeagleBoard by changing the content of the on-board Flash (eMMC) or by forcing it to boot from the microSD card. It's not very clear from their documentation how easy or hard it is to create your own memory images (for SD card or the eMMC). I suspect it's not trivial.

I have a simple non-preemptive RTOS that uses only one hardware timer, so: YES, of course you can do that with one timer.

Just configure that one timer to keep track of time, and you can at appropriate points in your software wait until the proper time has arrived to do the next thing.

A minor inconvenience can arise when your timer rolls over, but assuming you inspect the timer often enough you can maintain an extension of the timer and increment this extension whenever the current timer value is lower than the previous one.