Re: How do I remove this faucet?
I would caution against just whacking the lines and installing compression anglestops. From the looks of it, this faucet is fed from the top, the faucet itself is attached tot he sink (nuts underneath the sink flange ). Unless your new faucet is of the same relative design - top fed - then you're going to have to reroute the pipes under the sink OR use extremely long supply hoses to reach from where you cut the lines and install the anglestops to the underside of the sink flange where the new faucet will be fed from.
As was mentioned, sweating new copper fittings and pipe is pretty darned easy. You'll need a torch - preferably using mapp gas (burns hotter than propane ). Turn off the water at the main and the water heater and drain down the lines before cutting them. A hacksaw will suffice if you don't have a mini-tubing cutter, you'll just have to scrap or sand off the burrs from cutting. Be sure to clean any tailings out of the inside of the pipe as well.
Another tip - Cut and dry fit all your connections first to make sure everything lines up where you want it. From there you disassemble, apply the flux, and reassemble. When you start sweating the joints, apply the heat to one side of the joint and hold the solder against the other, when the solder flows, it will "pucker" all the way around the joint. When you're done, wipe down the joints and the pipe to remove any excess flux because the excess will cause corrosion and possible problems down the road.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!