Order of RC sacraments taken?

You are BOTH right. Well, almost.

For children, your order is common in the West, but not mandatory. In fact, there is a diocese in Arizona (Phoenix, I think) where kids are baptized as infants, go to confession at or 8, confirmed at 8 and then receive their first Holy Communion at their confirmation Mass. So your friend is correct also.

For adults who are not baptized, the order is baptism, confirmation, first communion (all in one Mass) and then confession.

For adults who are baptized, the order is baptism (usually their original baptism counts), then confession, and then confirmation and first Holy communion at the same Mass.

The bishop sets the age of confirmation, but it cannot be younger than age 8. My son was confirmed at age 10 (Diocese of Lincoln). My sister's kids were not confirmed until age 16 (Diocese of Arlington). Our diocese confirms kids young because the bishop believes that kids need the graces of confirmation to get through adolescence.

You're correct. Baptism is first, then Confession, followed by the Eucharist and Confirmation. Then, if you decide to become a priest, Holy Orders. If you decide to marry, Matrimony. Usually, the last sacrament is the Anointing of the Sick; ideally just before you die, since it increases your chances of making it to heaven.

you are both right.