Isn't that a solid copper tube going upwards? It isn't going anywhere while still attached at the other end. At least, not easily. To remove the faucet you would loosen the two retaining nuts under the sink, that is the big flat ones that are flush against the bottom of the sink and are threaded around the metal where the water goes in. Probably you will need a basin wrench for this.
https://www.harborfreight.com/12-inch-basin-wrench-91958.html
Hopefully the retaining nuts are not corroded or covered in calcium deposits, which makes them harder to remove. Then lift the whole faucet up with those two pipes coming out with it. You might have to loosen the nuts at the top of the supply lines and take the pipes off, but probably not.
Given your stated skill level, you will put the replacement faucet on (maybe with a base of plumber's putty, or a supplied rubber mounting piece, the faucet will have instructions), tighten the new retaining nuts, and then connect it with flexible supply hoses. Get the braided ones, they are less prone to bursting. Your current set up is better, as that copper is unlikely to ever burst, but you won't know how to make that fitting. Take the whole old one to the store, pipes and all, and somebody in the plumbing department will help you get the right pieces. In particular, the faucet needs to have a similar geometry for the water inlets to your old one or it won't fit on the sink, and the supply lines obviously need to be long enough to reach. It would also be a good idea to measure the space around the faucet before removing it, as you might encounter a replacement faucet which has the correct geometry but wouldn't fit this particular sink, as in extending too far back and hitting the wall, or hanging over the sink.
Also, don't mess with the nuts on the shut off valve unless the water is off to the house. You probably do not need to replace those. It isn't uncommon to have to replace the washer for the valve and the packing in the cap. That isn't hard. Newer installations usually use 1/4 turn shut offs, with ball valves, which have no rubber washers. Verify that your shut offs really are shut off all the way before working on this faucet. Open the faucet on both sides and shut off at the shut offs. If the water won't stop dripping out of the faucet you either need to fix the shut offs first or just turn off the main water supply and don't worry about it for now. Rather than change the washers you could replace them, but for your stated skill level, I wouldn't. They may be very hard to remove and you could mess up the pipe coming out of the wall, and at that point you will be calling a plumber.
Why is that wall wet?
