If medically necessary it is permitted to wear a medicinal patch or bandage under the Rezuah Shel Yad/Hand Tefillin Strap. Someone who, G-d forbid, broke their arm continues to place Tefillin on the broken arm (the Halachic authorities only have a doubt if the arm is permanently paralyzed).
If the cast is only on the arm and not on the bicep, then one makes a Bracha/Blessing and puts the Tefillin on the bicep and wraps the strap over the cast. If the cast covers the bicep the Tefillin is placed on the bicep (and wrapped around the arm) but without a Brachah. Even in such a case a Brachah must be made on the head Tefillin.
There should be no writing on the underside of the Straps. Some Rabbis consider long bangs to be a separation between the Tefillin and the head. A person should also take in to consideration that it is hard to keep the Tefillin in the correct place if it is resting on long thick locks of hair.
The underside of the Retzuos must rest against the arm and the head. No part of the Retzuah/Tefillin Strap may be flipped over that the underside is visible.