Is it obligatory to perform a full-body ghusl if a slight trace of feces is found on clothing after waking up, given that its excretion was not felt, and is repeating the 'Isha and Fajr prayers valid?

A full body ablution (ghusl (definition)) is not required for passing stool. If it is suspected that stool was passed either before or after the prayer, its expulsion is presumed to have occurred after the prayer, and thus the prayer is valid and does not need to be repeated. If the impure area is washed and the prayer is repeated, one has fulfilled their obligation. However, if there was residual impurity from a previous purification, the prayer is valid and does not need to be repeated.