Does a very small amount of discharge that exits after ablution invalidate it? And is ablution valid by placing an adhesive strip over the vaginal opening to prevent anything from exiting, and praying several prayers with this ablution, especially given the difficulty of renewing ablution due to paralysis and the approaching performance of the Hajj pilgrimage?

Islamic Sharia (definition) is built upon ease and does not aim to place people in hardship or difficulty. Your situation does not necessitate placing adhesive tape; rather, it is a whisper from Satan. A Muslim is not required, after performing ablution, to inspect himself to see if anything has exited him or not. Instead, he should perform istinja (definition) (cleansing after relieving oneself), then sprinkle some water on his private parts, perform ablution, pray, and not pay attention to these whispers. Al-Hasan (definition) al-Basri was asked about wetness after ablution and istinja, and he said, "Ignore it." Sheikh Ibn Uthaymeen emphasizes turning away from these whispers and not paying attention to them, unless one is certain that something has exited, in which case it is necessary to wash whatever was affected by urine and repeat the ablution. If you are not certain that anything has exited, then you are still in a state of ablution and purity.