How can one emulate the Prophet (peace be upon him) in fasting most of Sha’ban, and what is the nature of this continuous fasting? Also, how can one determine the few days that the Messenger (peace be upon him) used to omit?

The Prophet, peace and blessings be upon him, used to fast all of Sha'ban, or most of it. There is no confirmed specific number for the few days he would not fast. Thus, whoever fasts all of it, most of it, or even a little of it, has followed the Sunnah.