What is the ruling on my prayer, seeking forgiveness, and repentance without performing ghusl or uttering the Two Testimonies of Faith, in the event of missing the Fajr prayer and being exposed to whispers of apostasy and involuntary internal laughter?

It is advisable to ignore apostasy-related whispers (waswas) and not pay attention to them, for you will not be held accountable for them, and they do not expel you from Islam. As for prayer, one must take measures to wake up for it. If sleep overcomes you and you do not wake up until after sunrise, then there is no blame. However, if you intentionally sleep through the prayer time until it expires, then you must repent, seek forgiveness, and make up the prayer, but this does not expel you from the faith. It is legislated for the one afflicted with whispers to adopt the easiest of opinions.