Is it obligatory to make up prayers and fasting due to masturbation and the subsequent emission of fluids?

What you are doing, masturbation, is forbidden, and you must repent to Allah for it.

If this act leads to the emission of semen and you were aware of its prohibition, then it invalidates the fast. However, if it did not lead to the emission of semen, or if you were unaware of its prohibition, then your fast is valid.

The emission of semen necessitates ghusl (ritual bath). So, if you prayed after the emission of semen by merely performing wudu' (ablution), then your prayers are invalid, and you must make them up.

If you doubt whether the emitted substance is maniy (semen) or madhiy (pre-seminal fluid), you may choose between the two and assign it the ruling of one of them.