1) I'd figure it might be hard to patch the UMD directly, but I do say, legally, that you should support the game makers by buying the game if you're well and able to. I own the physical version as well, myself, and I enjoy having it. (I also own Makai/Phantom Kingdom Portable, which is another game I wish could be translated.) You may need to find the iso, but Chep has put down which version exactly you'd need. Just google it.
2) The main game is, for all sense of the word, complete and playable right now. Chep is currently working with Sardine-Queen to translate the bonus chapters and extra dialogues. It's entirely playable right now by all sense of the word, other than some proofreading required (which I'm assisting with as I go through the game.)
3) Yes, the main game translation is based off of the original uncensored NA version of La Pucelle. However, as far as I know, the gist of the script between both the Japanese version and the American version are basically the same. The main points of censorship in the NA version of La Pucelle mainly had to do with religious imagery and smoking, which tend to be weird points when it comes to Western standards. I think as far as the main story goes, that will be unchanged, unless if Sardine-Queen makes any suggestions (since she's the one who's handling the translation of the Overlord Prier chapters).
It's better to ask than to assume! Just enjoy the game when you can, okay?