1) I'm not disputing that it was wrong for UK to evict the Chagossians. I'm only disputing that the Chagossians have some sort of fundamental human right to return all these years later, just because their grandfathers used to live there.
2) Yes, many leading philosophers of previous centuries used to think very highly of property rights, but this trend has greatly diminished in the last 50 years or so, especially in Anglo-American political philosophy.
In any case, I'm pretty sure that if I offered a significant premium over the prevailing market price, most people will be happy to sell their home and move elsewhere. Especially if I also offered to cover their cost of moving and lost wages while they look for a new job. (That's roughly what I think every government should offer when they need to relocate people.)
3) I totally agree. It was wrong for the UK to move them without their consent. But what is done is done, and now it's time to ask what to do about it.
If I break your phone, property rights mean that you have the right to make me compensate for your material losses. It doesn't mean that you have the right to make me restore your broken phone to its original condition, no matter how much sentimental value it might have had for you.
4) That's a genuine problem. If it is impossible to ensure an equal or greater quality of life for the relocated population, perhaps that's a good reason not to relocate them in the first place. On the other hand, I find it hard to believe that a country like UK would be unable to arrange a fantastic life (at least materially) for a few hundred islanders no matter where in the world they were. They were simply unwilling to do it, just as they were unwilling to consult the locals before deciding to lease Chagos to the Americans.
tl;dr: Something very bad happened. But making it right is not simply a matter of resetting HEAD to a previous commit.