Have I committed a sin by breaking my fast on one day during a two-week fast I swore to observe, and is fasting on Saturday acceptable?

The ruling on fasting Saturday alone has been previously explained. If you intended to fast for two consecutive weeks, then you must do so. However, if you intended to fast for fourteen days without stipulating continuity, then you are permitted to break your fast during this period and then complete the number of days. As for fasting Saturday as part of fasting two consecutive weeks, there is no harm in it by agreement.