Is a disruption in the sequence of making up prayers considered a valid make-up, given the general intention to make them up, sometimes interrupting them out of shyness, lacking devotion in them, not comprehending what is recited, and some of them being performed quickly? Is this make-up acceptable?

The preponderant opinion is that doubt concerning an act of worship after completing it does not affect its validity. Any prayer about which you doubt having missed a condition or a pillar, without being certain, does not require you to make it up. The absence of devotion (khushu') in prayer does not invalidate it and does not necessitate its repetition. Prayers in which you missed a condition or a pillar do not require you to repeat them, according to many scholars. As for the prayers you have already made up, you are not required to repeat them, because the preponderant opinion is that there is no obligation to observe a sequence between missed prayers, while cautioning against obsessive thoughts (waswas) and advising to disregard them.