Can taking a calcium supplement help heal a broken broken bone faster? If so, how much can be taken daily? And can any other vitamin/mineral help?

No. Your body will get calcium from other areas to heal a fx. So while it will not directly help heal faster, it is likely a good idea in general to take calcium supplements, especially women.
Not speed it up. It will not speed it up. Bones heal even in starving people. At ur age u should have adequate ca reserves on an adequate diet. Ur daily intake 4 ca is 1600mg & vitamin d of 2000iu. If u feels that u r deficient , take supplements. But u have 2 consider all ur sources of each.