Are my fasts valid and accepted,
if I didn't wake up for Fajr.
When I wake up, I drank Water and Started my Fast.
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If you didn't wake up before Fajr and then you wake up after Fajr then you can't eat or drink. If you ate or drank after the time of Fajr then your Fast is not going to be a Fast. In Quran 02:187 it said like this:
وَكُلُوا وَاشْرَبُوا حَتَّىٰ يَتَبَيَّنَ لَكُمُ الْخَيْطُ الْأَبْيَضُ مِنَ الْخَيْطِ الْأَسْوَدِ مِنَ الْفَجْرِ ۖ ثُمَّ أَتِمُّوا الصِّيَامَ إِلَى اللَّيْلِ
Translation: and eat and drink until the white thread (light) of dawn appears to you distinct from the black thread (darkness of night), then complete your Saum (Fast) till the nightfall.