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To clarify, when you say cutting out did it feel like the transmission was slipping or the engine was stalling?
From the look of those codes it sounds like the transmission valve body has a faulty valve or solenoid. This wouldn't normally cause the engine to stall. You would get a flashing transmission temperature light though.
Oh sorry, the phone call pop up is automated. Not generated by me.
If in fact the transmission is the issue, I would probably start with replacing the transmission valve body (if the fluid level looks normal and the fluid isn't burnt looking).
If it's not really the transmission causing the problem I would watch for additional trouble codes to set that might explain the stalling you are experiencing.
There is no easy way to check the levels.
The only reason you would really need to check is if there are signs of an external fluid leak. As long as there don't appear to be leaks you shouldn't have to remove the check plug. However, if there is a fluid leak you can check as follows:
Please let me know if you need additional info.