Can I fast for two months as an expiation on behalf of my grandmother who broke her fast during Ramadan while she was pregnant, based on advice, and what should I do concerning menstruation periods?

The one who breaks their fast on a day in Ramadan without a valid excuse must make up that day. If the breaking of the fast was due to intercourse, then they must make up the day and offer expiation. However, if it was due to something other than intercourse (such as intentionally eating or drinking), scholars have differed: some say that only making up the day is required along with repentance (the view of the majority), while others say that both making up the day and expiation are required (the view of the Malikis).

Therefore, your grandmother is only required to make up the day along with repentance. However, if you offer expiation on her behalf by feeding (feeding sixty poor people), it would be better. Fasting is also valid for her, and menstruation does not interrupt the ruling of consecutive fasting.