Answered by Sayyidi al-Ḥabīb `Umar bin Hafīẓ (may Allāh preserve him and benefit us by him).

Is it possible for a seeker to enter khalwah (spiritual seclusion) without the supervision of a shaykh?

This is like someone taking medicine without the supervision of a doctor. There may be general benefit in taking the medicine, but the patient will not receive full treatment without the supervision of the doctor.