Can women recite Ashtakshara mantra after Samashrayanam or should it be recited only after performing Bharanyasam?

Women can very well recite Ashtaksharam after Samashrayanam.
Mantra upadesam is done only during Samashrayanam; it is a must to recite this mantra if one has obtained upadesam through an Acarya. It is a part of the daily austerity.