Greetings Merry Mary!
I was hoping a plumber might've written in on this topic by now. I have looked at these pictures a number of times and it is kind of ugly! If I'm seeing the pics correctly, I don't think the faucet is welded to the sink--it just seems that way.
One of the things I always find tough about working under sinks is the uncomfortable working position. Is it possible to (obviously, with the water shut off): cut the supply lines (maybe a foot below the sink) and disconnect the drain, and take the sink off? Then you could turn the sink upside down to work on it. Obviously this leaves you to deal with putting down the sink again later--this may or may not be a big deal depending on countertop surface, etc.
Removing the sink would hopefully allow you to hacksaw off the old faucet parts. There should be a place to hacksaw that would leave only a single nut on each side to remove, freeing up the faucet. Or saw right through each of the pipes right under the sink; the faucet should then lift right out from the top.
When you put it back together, you can do so in a more conventional manner--with flexible supply lines from the shut-offs. (You'll probably need some new fittings.)
This is kind of a tough 'first project' for a new homeowner. You might run into some difficulty but it should be within your ability. And I still have hope there'll be some additional posts on this topic. Good luck.