Is it obligatory to be extremely meticulous in removing dirt from the nails and navel, and avoiding any trace of blood or impurity for fear of invalidating ablution (wudu') or ritual bathing (ghusl)? And must a worshipper hear himself during silent recitation? And is the invalidation of ablution, ritual bathing, and prayer due to obsessive doubts resulting from fatwas justified?

The cure for obsessive doubts (waswas (definition)) is to ignore them and pay them no mind. What you are doing, such as exaggerating in ablution (wudu') and ritual bathing (ghusl (definition)), cutting nails, and washing the navel, is extremism and fanaticism in religion. Wudu' and ghusl do not take a significant amount of time. A small amount of blood is excused, and doubts about impurity should be disregarded, building upon the original state, which is purity.

For recitation and takbir (pronouncing "Allahu Akbar") in prayer, it is sufficient to move the tongue and lips and articulate the letters from their proper points of articulation; it is not a condition for the worshipper to hear themselves. The voice of a non-mahram (definition) woman is not considered 'awrah (something that must be covered or concealed) unless there is softness in speech or it leads to temptation.

Sufficient bowing (ruku') is to bend so that the hand touches the knee. Complete bowing is to place the hands on the knees while keeping the back straight. There is no need to repeat previous prayers whose validity is doubted due to ignorance, because Allah has forgiven mistakes and forgetfulness.