Is my prayer valid if I joined the Imam between bowing and standing without certainty, then forgot to perform the rak'ah that I considered missed, and only remembered it after the first tasleem, so I performed the rak'ah before the second tasleem, knowing that there is a difference of opinion regarding the sufficiency of the first tasleem to end the prayer?

If you are not certain that you caught the Imam in rukoo’ (bowing), then that rak’ah (unit of prayer) does not count. If you doubt catching it, you must make it up and perform the prostration of forgetfulness (sujood as-sahw). Your making up of that rak’ah is valid. As for your salam (salutation) before completing the prayer, it is an act of forgetfulness that does not invalidate the prayer. Rather, the prostration of forgetfulness is prescribed for it, and it should be performed after the salam. If you do not perform the prostration of forgetfulness due to forgetfulness or ignorance, your prayer is still valid and not invalidated.