Is the feeling of anxiety and trembling before leading the prayer, followed by calmness after the first Rak'ah, considered an illness or hypocrisy?

What you are experiencing stems from shyness and fear of people noticing you. To overcome this, it is advised to have self-confidence, not be bothered by inadvertent mistakes, and strive for humility (khushu') and excellence in recitation. If what you are experiencing is due to showing off (riya'), please refer to Fatwa No. 46511.