Is doubting oneself after hearing the aforementioned Hadith about the first people to be thrown into Hellfire, and the fact that I no longer pray aloud, and that I discuss everything with myself before doing it, considered to be intrusive whispering (waswasah) or self-rectification?

Holding oneself accountable, seeking piety, and avoiding ostentation are all matters prescribed by Islamic law. However, one must be cautious not to let these turn into obsessive doubt, as this is from the work of Satan. It is sufficient to strive for sincerity in one's deeds and supplicate to Allah that He accepts them. Lowering one's voice in supplication is permissible, as the Prophet (peace and blessings be upon him) forbade raising the voice when supplicating.