Question

Recently a certain righteous man passed away, and many saw him as the leading sage of the generation, or gave him other similarly distinguished titles.
In recent years he also gave practical instructions to the public in a variety of areas,
which were, how shall we put it delicately, not really accepted by many sensible people.
Immediately after his death, many wealthy people wanted to buy his belongings, such as his lectern or handwritten manuscripts and the like.
The price: many millions of dollars for items, a business for rich people who see value in this. (It was reported that the lectern was sold for $7 million.)
In the last 9 years, one of his sons moved to live in that righteous man’s home, and everything was run under his auspices there. Of course, the purchases after he went the way of all the earth are also being handled through him, since he lives there.
According to what was published, the other brothers cried out: where are we? And they sued the brother who lives there, demanding that he share the inheritance with them.
At the religious court in Bnei Brak, he produced a letter in which that righteous man bequeaths to him everything he has…
The date: 9 years ago, when he moved in with him and managed everything.
The brothers are crying bitterly: but it is well known that by then our father was already “not at his best,” and this will has no validity, and he must give the brothers their usual share.
So there is a mess going on. (At the end of the day, it really is a lot of money.)
 
My questions:
1. Is it permitted to buy an item that a righteous man used? To pray to this lectern? Just to keep it as a charm for protection?
2. Is it permitted to say about a person that in the last decade of his life he was “not at his best”? Is that insulting? Is that a desecration of the honor of Torah?
3. From when does writing an inheritance no longer count as a real legal act? If a person is a bit tired? Completely insane? Doesn’t understand exactly what he is saying or what is being said to him?
4. Do his halakhic and ideological instructions have any validity at all in those years?