How can a 16-year-old student increase their connection with Allah, their devotion, and their certainty in prayer, to overcome the feeling that their prayer has no effect on them when committing misdeeds, and their suffering from obsessive whispers about the existence of Allah?

The cure for intrusive thoughts (waswas) is to ignore them and pay them no attention, knowing that they will not harm you as long as you dislike them.

As for sins and transgressions, all humans are fallible, and their cure lies in sincere repentance, increasing good deeds and acts of obedience, and maintaining prayer with humility, fulfilling its conditions, pillars, and obligations.

Strengthening one's connection with Allah is achieved by frequently remembering Him, reciting His words, being mindful of Him, contemplating His names and attributes, reflecting on the Last Day, and associating with righteous people.