Howdy and welcome to AIRforums, JR! You came to the right spot to ask any questions about your new-to-you Ambassador.
You're right, the exterior looks pretty nice! And the interior, while it needs some things RE-hung, REpaired, and even maybe REplaced, it doesn't appear to be terribly dirty, like some of them are. All in all, it looks like you have just bought yourself a nice new hobby!
Of course, as Twinkie says, you are probably best off if you replace all the copper with PEX, but that isn't always the case. Last winter I didn't properly drain the shower wand hose, and that left a bit of water in a 5" piece of copper behind the wall in the shower, directly behind the shower valve.
Lucky for me, I just didn't use the shower, and that eliminated a water leak until I could get some time to take the bath apart and figure out what went wrong. What I did starts at this post
I didn't find that removing the two rear panels of the tub was a big deal, and I can't remember seeing any pipes that would need to take the actual tub out. Taking the tub out WOULD be a bigger job, that's a fact, but what I did could be done by most anyone. In fact, you will see the little pipe I'm talking about. I put an arrow to it in one photo. That job was my first-ever pipe soldering!
So, all that to say, maybe it's just one pipe like I encountered, or maybe it's a bunch of them. Once you start to look at the copper, you should be able to tell pretty quick, since a burst pipe does NOT "hide it's light under a bushel", as the old saying goes. You can see splits and bulges, even at my advanced years.
Let us know what you decide to do, and like you have started to do, don't spare the photos!
Two last points: the first thing we always recommend to new folks is to get the outside all sealed up so that no more leakes can happen. Very important, because leaks can make more work for you faster than you can fix things up.
Also, I'm guessing from your photos, that you will be looking for new axles pretty soon. Take your time on that one though, it's a popular subject here, and you want to be able to savour it properly...