Is it permissible not to stick out the tongue during prayer when reciting Tasbeeh, Quran, and supplications in colloquial Arabic? And is changing a supplication after insisting on it considered a lack of wisdom and confusion, especially after believing that being blessed with supplication means Allah's granting of success?

The servant cannot be considered a supplicant, reciter, or rememberer of Allah in prayer unless they move their tongue and lips and pronounce the letters from their proper articulation points. Scholars differed on whether it is a condition to hear oneself; the majority view is that it is, while the Malikis and Ibn Taymiyyah hold that moving the tongue is sufficient, even if one does not hear oneself. Not moving the tongue in prayer is not considered remembrance (dhikr) or supplication (du'a) and the prayer is not valid with it. As for outside of prayer, uttering remembrance with the heart is rewarded, though the concordance of the heart with the tongue is more complete. Asking Allah and supplicating to Him is permissible, and if a benefit appears in something other than what you initially supplicated for, and you supplicate for that other thing, there is no harm. It is better to entrust the matter to Allah and ask Him to facilitate good wherever it may be, while being cautious not to ask for something specific whose goodness is unknown, and if you do ask for it, then qualify it with the condition of Allah's knowledge of what is best, and perform Istikhara (prayer for guidance) beforehand.