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The stated capacity is 4.2 liters. That is about 4.5 quarts, so there should be a little over a gallon including the filter.
The bundled hoses on the left side of the motor are various drains and vent hoses. They go somewhere at the top, but shouldn't be connected to anything at the bottom.
As far as the oil disappearance, I don't have a lot of ideas. TT600s are sturdy beasts, and they typically don't use oil. There are a few places that oil might leak. The stator wiring sometimes leaks if it wasn't installed right. The output shaft can leak, especially if the chain has been run too tight for a long time. I think there was a report of a leak from the gear shift shaft, but I don't remember for sure about that one. The only way I can imagine that your bike got bone dry is if it didn't have oil in it from the shop, but I don't know why the low oil light would not have practically jumped off the instrument cluster and beat you over the head if you were running without oil.
Did you find evidence of leaks under the bike? If it burned that much oil, you should find a whole lot of oily residue in the exhaust pipe.
Keep us posted on how things go for you, and good luck finding the problem.
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