Is it permissible for me, as a Muslim woman, to pray 'Isha alone at home when its time begins, or must I wait for the Adhan, especially if it is delayed?

After verifying that the time for prayer has begun, it is permissible to perform the prayer even if the muezzin has not yet recited the adhan. It is better for a woman to hasten to perform the prayer at the beginning of its time if she has verified that the time has begun, because prayer performed at its proper time is among the most beloved deeds to Allah.