Is a make-up fast required for someone who deliberately broke their fast by masturbating after intending to fast, and deliberately omitted prayers on the same day or other days, and does this entail a make-up?

You must repent to Allah Almighty for masturbation, breaking the fast, and intentionally abandoning prayer. You must make up all the days on which masturbation occurred and semen was emitted; no expiation is required. Intentionally abandoning prayer is a heinous and grave sin, and you must make up all the prayers that were intentionally missed. If the number is unknown, continue making them up until you are reasonably certain that your obligation has been fulfilled.