they don't need to give you a copy when you check in but they are required to file one. Sounds more like they haven't filed one if they're behaving like that. Call their bluff and say you're going down to immigration and you'll give their hotel name and number to the office if asked. Might not have any impact but it might scare them into giving you a copy, assuming they've filed one for you that is.
nothing is stopping you from going before 1 October. Just ask them for a copy of the TM30 as they are required by law to file one within 24 hours of your arrival with them.
sounds more like he's leaving the hotel before going to immigration therefore they don't need to give him a TM30. If he went today, and he was still at the hotel, then they would as the OP has stated.
it expires when your re-entry permit expires as you must've had a single entry visa. Therefore the re-entry permit allowed you to leave whilst keeping your student visa valid. Failure to return by the expiry date on your re-entry permit will automatically result in your student visa being cancelled.
Whatever visa/extension of stay you're currently on will become invalid if you don't return by the 26th. If you're on an extension of stay based on employment then you need to speak to your employer as your right to work in Thailand will be revoked if you don't return by that date.
To solve the flight issue book your Turkey flight for whenever you're planning to use it.
Then either buy a cheap throw away ticket to SG or Phnom Penh (wherever is cheap basically) to show you're leaving Thailand before your tourist visa or visa exemption expires or buy an onward ticket from a website which deals with them. I haven't used any but others have, Google will have plenty of suggestions for this part.