How can one make up prayers concerning whose validity the questioner is in doubt, due to not reciting with the Imam in silent prayer, or not catching the rak'ah before rising from rukoo', or not reciting the tashahhud after catching up on missed rak'ahs, or the lower back becoming uncovered during prostration?

The prayers in which you did not recite with the Imam do not obligate you to repeat them, because the majority of scholars hold that recitation behind the Imam in silent prayers is recommended, not obligatory. Reciting the tashahhud once after the two rak'ahs you missed is correct, so you are not obligated to repeat prayers of this nature. If a small part of your awrah was uncovered during prayer, it does not harm it, and similarly if it was a large area and you promptly covered it. Prayers in which it is certain that a condition or pillar was omitted, the majority of scholars obligate their make-up, and similarly for prayers deliberately missed, the majority are of the opinion that their make-up is obligatory.