Is it obligatory to fast to fulfill a vow, and is it permissible to fast the first ten days of Dhu al-Hijjah with the intention of making up for a vow, and what do you advise for expiating sins for those with a weak ability to abandon what angers Allah?

This vow is called a "vow of contention" (Nathr Lajaj). Scholars have differed regarding the ruling for one who does not fulfill it. Some have mandated an expiation for breaking an oath (kaffarat yamin (definition)), while others have given the option between fulfilling the vow or offering the expiation. Therefore, there is no harm upon you in offering the expiation for breaking an oath, and there is no harm in fasting the first ten days of Dhu al-Hijjah with the intention of fulfilling the vow.