How can one perform prayer and ablution with a full cast on a broken right hand?

If you want to perform Wudu' (ablution) or Ghusl (ritual bath), wash the healthy parts of your limbs, and wipe over the splint; this will suffice you. As for prayer, perform it to the best of your ability, for what you are unable to do is waived from you, such as placing your hands on the ground during prostration, or raising your hands when saying "Allahu Akbar" (Takbir), or placing your right hand over your left, due to the Almighty’s saying: "So fear Allah as much as you are able."