Is it permissible for me, due to polio and the inability to stand up, to perform ablution before Fajr without rinsing my mouth and using a small amount of water to pray in bed, then in the morning put on my brace and perform a full ablution with wiping over my socks or shoes, and is it necessary for me to repeat the ablution before putting on the brace in the morning?

If a woman who is experiencing bleeding [istihadah] performs ablution (wudu') on the bed with a small amount of water due to hardship, her ablution is valid, provided that she makes sure to apply water to every limb, so that the water flows over it, not merely wiping. Rinsing the mouth (madmadah) and sniffing water into the nose (istinshaq) are confirmed Sunnahs, and some scholars consider them obligatory. Wiping over the leather socks (khuffayn) is permissible if they were worn after a complete state of purity (tahara), and its duration is one day and one night for a resident and three days and nights for a traveler, unless a state of major ritual impurity (janabah) occurs or they are removed. If she wiped over the khuffayn or socks without having worn them in a state of purity, she must repeat the prayers she performed with that wiping.