Is it permissible for me to postpone making up many mixed prayers (between what was due to a valid excuse and what was not due to an excuse), and is it valid to make them up with a general intention without distinction or order?

The questioner is not obligated to repeat the prayers he performed as make-ups after their time had expired, if he had indeed made them up. However, if the prayer time expired because he did not hasten his walk and was preoccupied with drying himself and repeatedly wiping, and thus did not pray, then he is obligated to repent and make up those prayers immediately. When making up prayers, it is necessary to observe the sequence between missed prayers and to specify the intention for each prayer. If he does not know the exact number of missed prayers with certainty, he should pray what he believes most likely absolves his responsibility. If he does not trust the knowledge of a scholar in his locality, he may contact those whom he trusts among the people of knowledge.