The break in period is to give the newly machined parts a chance to get to know each other better.
The finish on the machined parts has peaks which actually touch each other through the oil film when the parts are new. By running the machine gently, you allow these intefering parts to polish each other off slowly without generating enough heat to cause galling of the sufaces or even worse, seizing up.
The accepted norm for running in is to do everything gently. Never "lug" at low rpm and do not maintain high rpm for long periods. It is good to rev occasionally to "stretch" the internals so that you do not create wear ridges at the limits of travel which you will find, disastrously, when you do wind it up after the run in period.
On 4 cycles, dyno oil is usually recommended for running in, as synthetic is so good it keeps the rings from seating. I would assume this is the same for a two cycle.
The deposits on the cylinder and head are just byproducts of combustion and are irrelevant until they get too heavy, then you have to pull the head and clean them off.
Hope this helps,