If I recently had a broken arm will the vibrations from a commercial flight cause damage?

No. Direct trauma might, but vibration at such low levels as those experienced during commercial traveling should not.
Not expected to.. Noi would not expect it to however be aware that swelling and pain may feel worse at times with a change in cabin pressure. Be prepared with medication on hand especially an anti inflammatory. Fyi I have never had a patient have an issue with internal hardware or fixation for a metal detector for an upper extremity injury.