Is it permissible to clip nails inadvertently after performing ghusl and donning the ihram garments but before passing the miqat? And is the 'umrah valid and accepted if a woman in ihram performs ghusl after menstruation, then performs ghusl for ihram, then discovers brown discharge and performs ghusl from it again before performing 'umrah?

A pilgrim is not required to enter ihram (definition) except at the miqat (definition). However, if one enters ihram from their home country, their ihram is valid, and they are obligated to avoid the prohibitions of ihram. If a person clips their nails before intending ihram, there is no penalty. But if this occurs after intending ihram, then the fidyah (definition) becomes obligatory upon them (fasting for three days, or feeding six needy persons, or sacrificing a sheep).

Regarding seeing brownish discharge (kudrah) after purification, it is not considered menstruation and does not necessitate a ghusl (definition). Rather, it only invalidates wudu'. Consequently, there is no need to make up for fasts unless she had broken her fast. The 'Umrah (definition) she performed during her period of purity is valid, provided it met the other conditions for validity.