As a woman, I get my period for one week. In that week during ramadan, I don't fast. In these non-fasting days, I must give zakat to the poor. What kind of zakat do I give? How much zakat should I give for each non-fasting day? I am a woman that does not have a job yet but has some savings.
You are confusing Zakat with Kaffara and Fidyah. Kaffara is due on a person who breaks their fast without a valid excuse, it is not due on those who have an excuse to not fast, such as a sick person or a traveler, they only have to do قضاء
فمن شهد منكم الشهر فليصمه ومن كان مريضا أو على سفر فعدة من أيام أخر
So whoever sights [the new moon of] the month, let him fast it; and whoever is ill or on a journey - then an equal number of other days.
Similarly, a menstruating woman is not required to pay it. Rather she needs to fast additional days to make up for those that she missed.
كان يصيبنا ذلك فنؤمر بقضاء الصوم ولا نؤمر بقضاء الصلاة
That used to happen to us and we were commanded to make up the fasts but we were not commanded to make up the prayers