Is it permissible to postpone prayers or abandon them until after completing one's studies and undergoing treatment for obsessive-compulsive disorder, given the severe suffering one experiences due to scrupulosity concerning purity and prayer, and its negative impact on one's time, studies, and future?

A Muslim is not permitted to abandon prayer as long as he is of sound mind. The matter is easier than you imagine; all you have to do is seek Allah's help and combat the whispers by not dwelling on them or paying them any attention.

Do not perform ghusl (ritual bath) unless you are absolutely certain that semen, which necessitates ghusl, has been discharged. Do not prolong your stay in the bathroom, and simply pour water over your entire body then leave. When performing wudu (ablution), do not wash any limb more than three times, no matter how much Satan whispers to you.

The matter of prayer is not difficult; it is merely a few minutes during which you stand before your Lord. Ignore the whispers, and whenever Satan deludes you into thinking that you have not recited or performed something, disregard his whispers and pay no attention to them.

Begin treatment now, for it will aid you in your studies and help you excel. Strive against the whispers, continue in obedience to Allah, and never neglect prayer. Know that repelling whispers is easy but requires sincere resolve and high spirits. Tayammum (dry ablution) is not sufficient when one is able to perform ghusl; therefore, you must perform ghusl if you are certain of semen discharge.