What are the expiations for sins and repentance, and how do we stay away from sin? And what is your advice for my mother, who makes many vows?

Among God's graces upon His servants is that He has made it easy for them to expiate their errors. Repentance is one of the most important expiators of sins, as are seeking forgiveness (Istighfar), righteous deeds, supplication (Du'a), charity (Sadaqah (definition)), and afflictions.

To stay away from sins, one should be mindful of God's watchful eye, feel shame before Him, fear Him, and remember the fate of the disobedient.

Regarding vows (Nudhur), making them is disliked (makrooh). However, they must be fulfilled unless there is complete inability, in which case one must offer an expiation like that for a broken oath (kaffarat yameen).