Are we allowed to recite the Quran loudly in obligatory prayers when we pray alone at home in the way imam does in the mosque?
There is the authentic hadith in which the Prophet, peace be upon him, said:
النساء شقائق الرجال
Meaning that women are the half twins of men regarding the acts of worship except if there is a specific exception such as adhan where it is only for men.
A woman can recite in a hearable voice in the salah “jahreya ” same as men, except if there are non mahram men around.
The woman’s voice is not awrah, yet usually we beautify our voices while reading Quran specially if we read with tajweed and this could be fitnah to men. This is in salah Jahriyah (prayers in which the Imam recites loudly in the first two rakaat). These are the Fajr, Maghrib, Isha and Qiyam layl prayers.