How can one get rid of the feeling of hypocrisy and the unacceptability of prayer, which leads to thoughts of abandoning it, despite being keen on performing it to the fullest?

The feeling of insincerity in prayer and hypocrisy that you are experiencing is a trick of Satan to turn believers away from good. Allah Almighty says: "He said, 'Because You have put me in error, I will surely sit in wait for them on Your straight path.'" To get rid of Satan's whispers, one must remember Allah, seek refuge in Him, not indulge in the whispers, and not pay attention to them. As for thinking about abandoning prayer, this is what Satan desires, and what is required is to stop these whispers and approach prayer with devotion, trusting that Allah will accept your deeds if you fulfill your apparent and inner obligations.