Is it valid to perform ghusl from janabah without rinsing the mouth and nose, and must one make up for the days that followed this ghusl if it was invalid?

Your ghusl (definition) (ritual bath) is valid, and there is nothing against you. Your delay in rinsing your mouth (madhmadhah) and nose (istinshaq) after bathing, and drying your limbs, does not invalidate it. This is because it does not contradict the requirement of muwalat (succession), the time interval was short, and sequential order is not a condition for ghusl. Furthermore, there is a recognized scholarly difference of opinion regarding the fundamental necessity of madhmadhah and istinshaq in ghusl. Your action of following the fatwa (definition) (religious edict) of a specialist whom you deemed qualified is permissible. Your fast is valid even if you did not perform the obligatory ghusl or performed an invalid ghusl, because ritual purity is not a condition for the validity of fasting.