Does prayer become invalid if a small amount of something exits—without lust—during it, with remembrance and looking, and is ghusl then required?

What exits from the two private parts (front and back) invalidates ablution (wudu') and nullifies the prayer. Your feeling that something exited during prayer and the presence of impurity (najāsa) on your clothes afterward means that something did exit from you during the prayer, and it is obligatory for you to repeat your ablution and prayer. If you repeated the prayer without ablution, then your prayer is invalid, and it is obligatory for you to perform ablution and repeat the prayer.