What is the ruling on the prayer of one who had a حدث (minor ritual impurity) before starting the prayer, but then led the people in prayer without a true intention, out of embarrassment before them, intending to repeat it at home? And is his action considered disbelief?

What you have done is a great evil, for which repentance is obligatory. It is not disbelief (kufr), but rather a major sin. It is incumbent upon you to repent to Allah Almighty, and that this act should not be repeated. You should know that Allah Almighty is more worthy of being ashamed before Him than people. So, His awe and fear should precede the fear and awe of anyone else.