2003 Ford Taurus will not Move

My aunt gave me a 2003 Ford Taurus with a suspected transmission issue. Though I am not so sure at this point. My wife likes the car, so I said I would see if it was worth fixing.

Report: Car was headed up a steep, bumpy driveway, a loud pop was heard and it would not go no more. It was backed down the hill and parked, where it sits now. I suspect it bottomed out as there is a severe oil leak along the oil pan.

Initial Inspection: Car will not go into forward or reverse. Shifter cable is moving the arm on the transmission. When I place it in gear, though the car will not move, I can hear and feel the engine bog down as if it's in gear, but acts as if it's in neutral regardless.

I checked the fluid in park, was well above fluid range on the dip stick as it should be. Though the car is slightly off level, I still let it run and checked it while running, no change in the level. It is possible the way it was sitting threw it off, or it wasn't completely up to temperature. Did not want to run it too long with an oil leak.

Removed driver side front tire, does appear to be some play, but it does not spin freely, just rocks back in forth. Not a lot of experience working on axles, so not sure what to look for. I did this in case it may be broken or disconnected from the transmission output. Either case, I cannot tell, though I see about a 1/2" gap between the large cylinder and the transmission. Not sure if this is normal or not.

Diagnostic thoughts: Given I can hear the transmission engage, I suspect the problem lies on the outside, or at least inside the bell housing. At first I suspected a broken axle, however, I cannot ignore the fluid levels, which I will likely check again after getting more motor oil. I also thought to check if the speedometer was moving as I give it gas. There are no computer codes.

Taking the fluid level into consideration, I would be prone to think it might be the Torque converter, or I understand there is a shaft that connects it and the fluid pump which could have broken (I understand this is common).

Questions: Is there a way to see if it is spinning between the transmission and the axle, without removing the axle? If tomorrow I find the speedometer moves, would that point more towards an axle? If it's the pump and/or TC, can this be changed without removing the transmission from the car? Are there any other tests I can do to help narrow this problem down to prevent me from doing unnecessary work? If the pump was not operating, would it still feel as though it was engaged when shifting into drive? (Based on the feel and sound of the engine)

Note that I do not have a shop, I am kind of a shade tree jack-leg mechanic that works on stuff only when I need to. Would take this to a shop, but I do not want to put too much money into this car. I also have noticed several times when mechanics in my area would say something needs a complete overhaul (new engine/transmission), resulting in hundreds or thousands of dollars worth of work, when the solution often ended up being a cheaper and semi-simpler thing to fix. I need to see if this is an issue inside the internal workings of the transmission before I go about fixing other things, such as the oil leak. Do not want to fix a bunch of minor things only to find out the transmission is in need of a rebuild/replacement.

Any help would be appreciated, thanks in advance.