Is it mandatory to cover head while praying?
Can a woman pray without hijab?
Can women do dhikr without hijab?
Can Zikr be made without covering of the head?– Youtube Islamic Academy | Ask Abu Saif
Yes, women can do all of those and also read Quran without wearing hijab. A woman should only cover up for salah. Regarding being “invited” by God, it just means that when God wants you to go, then He will make the means possible.