Praise be to Allaah Who has guided you to Islam. We ask Allaah to increase you in faith and guidance.
Yes, it is permissible for a woman to observe i’tikaaf in the mosque, indeed i'tikaaf is Sunnah for both men and women.
See question no. 37698
It is better to oberseve i'tikaaf for the full ten days, because this is what the Prophet (peace and blessings of Allaah be upon him) used to do. Al-Bukhaari (2026) and Muslim (1172) narrated from ‘Aa’ishah (may Allaah be pleased with her), the wife of the Prophet (peace and blessings of Allaah be upon him), that the Prophet (peace and blessings of Allaah be upon him) used to observe i’tikaaf for the last ten days of Ramadaan, until he passed away, then his wives observed i’tikaaf after he was gone.
If a Muslim cannot observe i'tikaaf for all of the last ten days, then he may observe i’tikaaf for as long as he can, two or three days or more or less, even if it is only one night.
Shaykh Ibn Baaz (may Allaah have mercy on him) said:
I'tikaaf means staying in the mosque to worship Allaah, whether that is for a longer or shorter period, because there is no report – as far as I know – to indicate a specific length of time, whether one day, two days or more.
Fataawa al-Shaykh Ibn Baaz, 15/441.