Those hoses are probably the lines for the trans cooler that go to the radiator.

 

There should be one hose that goes to and one hose that comes from the cooler. There is another fitting that will be for the breather tube/vent. It should have a hose attached to it (1/4" vacuum line works great if I recall). I actually extended mine up into the engine bay and put a small filter at the end of it. This will prevent any junk or water from getting in.

 

Sounds like a pump leaking at that rate. This is not common

 

I have been reading up on the maintenance manual for the RE5R05A 2002-2007. I see there are about 6 o-rings:

one o-ring on the input shaft after you remove the torque converter
one large o-ring that surrounds the pump
four o-rings that are exposed on the input shaft after the pump is removed

Should I look for anything else to replace? Also, I'm having a difficult time finding the replacements for these, what is a good source for these? It looks like I'll have to purchase a special slide hammer to remove the pump from kent moore, they are about 200 bucks.

 

I went ahead and found an overhaul kit for $213 and bought it. It has all the gaskets, rings, and seals. I'm going to have a transmission shop install since I don't have the special slide hammer and measuring tools.

I'll be replacing the radiator and hoses in the meantime. Should I replace the torque converter?

 

I took it to a shop and had them replace the pump seal, front seal, etc. They called and let me know that the bushing was shot, and it damaged the oil pump and the torque converter. So they replaced the pump and resealed it. I have a remanufactured converter I'll install. I'm hoping the shot bushing is the culprit.

 

If the fluid was too low, it could have contributed to the issue. Hopefully you now have it all done and can get many more miles out of it.