Yes, a woman can perform itikaf for gaining rewards and coming closer to Allah. If she is married, she will need the permission of her husband to perform itikaf. Itikaf is also sunnah for women in the last 10 days or Ramadan from sunset on the 20th of Ramadan until the crescent of Eid is sighted , or nafl if she does it any other time.
If a woman does itikaf for less than 10 days for example, 3 or 4 days in the last 10 days of Ramadan then this will also be considered as a nafl itikaf. She will have to perform itikaf in the specific place where she prays her salah at home.
If there is no such specific area then she can appoint a specific place in her home and make itikaf in that area.
If a woman prays salah in one portion of her home, but wants to make itikaf in another portion of her home, then before sitting in itikaf she should make the intention [niyyah] that from now on she will pray salah in this place then this will be correct and permissible for her to do so.
A big room cannot in its entirety be designated for itikaf, but a small room can. However, a space comfortable enough for her to sleep, eat and sit can be designated in a big room for itikaf. This area will be like the masjid for the woman. She cannot exit this area without a permitted excuse.
In a complete sunnah itikaf, which starts from sunset on the 20th of Ramadan until the crescent of Eid is sighted if she gets her menstural period [haidh] then she will abandon her itikaf.
However, she will be required to make up [qada] one day of itikaf with fasting from sunset to sunset 24 hours. No matter when her complete sunnah itikaf breaks whether two days remain or eight days remain , the qada will only be for 1 day.
If she become clean while Ramadan remains she can complete this qada of 1 day then and the fast of Ramadan will suffice her. If Ramadan has finished then she can make it up another day when she is making up her missed fasts, and if not then, then whenever she keeps a nafl fast. Yes, she can do it for any number of days. However, this will be regarded as a nafl itikaf since a complete sunnah itikaf will be one that is from sunset on the 20th of Ramadan until the crescent of Eid is sighted.
Yes, if she intended the complete sunnah itikaf from sunset on the 20th of Ramadan until the crescent of Eid is sighted but broke it or it was broken due to her menstural period [haidh] then she will make up [qada] for 1 day. She will stay in her designated place for itikaf unless there is a need to come outside of it such as relieving herself or for the purpose of food and drink.
If there is someone who can bring her food and drink, then it will not be permissible to leave for this purpose. According to need it will be permissible to have some wordly discussions, however, she should try and maintain the true spirit of itikaf by turning towards Allah and cutting herself off from unnecessary wordly talk.