Is it permissible to continue simulating congregational prayer without intention or ablution due to obsessive doubts and fear of exposure, while re-performing the prayer alone at home before its time expires? And does that affect the validity of the congregational prayer?

It is not permissible to outwardly perform the prayer while not actually praying, as this is an infraction and stems from succumbing to obsessive whisperings (waswas). Rather, one must rid oneself of these whisperings by performing ablution normally and praying with the congregation without paying attention to them, and by having the will to strive against and overcome them.