What should I know if I want to move from microcontrollers to microprocessors?
The main difference in these systems is that they generally do not run the majority of directly out of flash -- instead, there will be a small program in flash that acts as a bootloader, and the program will then be copied from some medium such as a SD card or SSD or hard drive into RAM, where it is then run from.  If there is a need to update the bootloader, there will be some means, either through the microprocessor or external, to update reprogram it.

So when you update your program, it will be downloaded to your system and then written to the SD card or SSD or hard drive, whatever you have.

When its running, there is really no difference between a microcontroller and a microprocessor.  It's just that in the latter case, there is a lot more RAM (perhaps several hundred MB) than you would find in a microcontroller.  The CPU doesn't care whether it is running out of RAM or flash.  One thing you do have to look out for: an errant program can wipe itself out in RAM, whereas this can't happen in flash.

Microprocessors will almost always have an external crystal as a clock source.  The processor may use a PLL (phase locked loop) to multiply the crystal frequency up to a much higher value (several hundred MHz or even a GHz).  This will be part of the initialization code.

Accessing peripherals is essentially the same as with a microcontroller; they're just external to the chip instead of inside it, so access is not as fast.  (The only "peripherals" typically on an x86 chip are timers, DMA, and interrupt controller.)  The processor communicates with the peripherals devices through I/O ports.