How do breakpoints work in C++ code? Are they special instructions inserted in between some assembler instructions when the code is compiled? Or is there something else in place? Also, how are stepping-through-the-code implemented? The same way as breakpoints...?
This is heavly depend on the CPU and debugger.
For example, one of the possible solution on x86 CPU:
Watchpoints can be implemented in the similar way, but instead of INT3 you put the memory page where watched variable is into read only, or into no access mode, and wait for segmentation exception.
Stepping through assembly can also be done by using trace mode. Stepping through source lines can also be done by placing breakpoints onto next instructions, based on debug data.
Also some CPU has hardware breakpoint support, when you just load address into some register.