@Alex *********
no, you definitely can't take a flight without passport. By law you have to have your passport or a copy with you and you have to give direkt access to the original if the police asks for. But usually there is no big deal if you are not suspected a crime like overstay.
Bus or train.
And if your passport is lost you need to make a report to the police. You are going to need the report for leaving Thailand, plus you need to go to your embassy. They will give you a departure permission. Went through that in the past.