What is the ruling on sleeping on a mattress that has slight impurity (such as dry drops of urine), and does that affect the validity of the prayer performed in the clothes one slept in, and is it obligatory to make up past prayers due to ignorance of the transmission of impurity through sweating?

The default is that ritual impurity (najasa) does not transfer and purity remains. So if you doubt whether something has become impure, the default is that it is pure, and certainty is not removed by doubt. Therefore, fear of sweating during sleep does not make your garment impure, because the transfer of impurity has not been ascertained. Consequently, you are permitted to pray in the garment you slept in, your prayers are valid, and you do not need to repeat them. Beware of obsessive whispers (waswasa).