I can't remove the hose from underneath...
What sort of faucet house connection is this, and how do I remove it?
At least the left two hoses are screw-on fittings. The right one looks like it has a threaded fitting at the top, but may be a push and turn connection at the hose. It's hard to tell from the picture. The screw-on fittings should come apart by turning the nut. However, it also looks like there may be some crud that could be locking things up, especially on the middle hose.
I wouldn't use the typical solvent-based products (like Liquid Wrench or WD-40), on water lines. It might help to stick a few drops of CLR on the threads, wait awhile for it to soak in, and add more. Give it some time to dissolve any corrosion and minerals.
Use a wrench on the faucet side of the pipe to keep that from twisting and a wrench on the nut to turn the nut. Start with the most accessible hose and get that out of the way to make it easier to work on the next hose. You can get some leverage by positioning the wrenches "one face" apart, wrapping your hands around both, and then squeezing them together.
To remove only the hose, I would first see if the outer collar (the part with the opening in the side) would unscrew to allow it being pulled down to release the inner sealing joint. Then pull down on the hose connection with slight wiggling and twisting.
I think the nut above is designed to clamp the faucet body to the plate above and is not part of the sealing mechanism.