I saw blood at night at Esha time. The next morning I didn't see blood and performed ghusl – after Fajr but before Dhuhr. Do I need to make up any prayers? If yes, then which ones? Also, if I haven't been making up such prayers please guide me as to how I can calculate my missed prayers for each cycle ever since I started menstruating, between the time I saw blood and the time when I confirmed I was pure.
بِسْمِ اللهِ الرَّحْمنِ الرَّحِيْم
In the name of Allah, the Most Gracious, the Most Merciful
Because matters are referred to their closest times, you will make up the prayers from the time you went to bed. When you went to bed at Esha time having seen blood, it is assumed that you became pure just before that salah time ended.
So, in your case, if you went to bed at Esha time, you will be required to make up Esha and Fajr.
If you have missed prayers in the past in the same manner, you must try your best to make an accurate estimate of how many prayers you missed, while sticking to the path of caution by overestimating slightly. As an example, you can multiply the number of Eshas and Fajrs missed over the past year in this manner and then multiply by the number of years you have been menstruating for.
Only Allah knows best
Written by Alimah Nasima Umm Hamza
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham
 Raddul Muhtaar, Kitaab at-Tahaarah, Baabul Hayd, Volume 1, page 291