Is the inability to sleep at night due to repeatedly performing silent Dhikr (remembrance of Allah) – out of fear of dying unawares and of shortcomings in the remembrance of Allah – considered a form of Waswas (whispers/obsessive thoughts), and how can one get rid of this to sleep well?

The believer fears death with a healthy fear that motivates him to prepare for it. The remembrance of Allah is good in all circumstances, but a servant should give himself sufficient rest, as Mu'adh said: "And I seek reward for my sleep just as I seek reward for my standing (in prayer)." Thus, the believer intends by his sleep to gain strength for obeying Allah and to gather himself for worship with energy.