This 125b cash is from BH, not from himself. He doesn't decide it all alone. If you want you can buy BH stock and follow along and be one of the shareholders.
It also isn't 125b cash, but 125b not in stocks, in possibly very liquid investments and well diversified.
I doubt it matters what he does with this money, unless you want to do the same. He completely missed the boat on the last ~10 years and I doubt he's the best example nowadays, his company is just very rich because for many decades he got the fundamentals right. You can as well invest like him if you learn what he knows, but I doubt you can get as rich as he did, because he did it in a different time.
He'll likely invest in businesses he knows, just like anybody investing should. Possibly brands, he's a big fan of businesses with a good brand and margins, who isn't? :-)
You mean, aside from building the largest solar power plant in the USA, and specifically calling out renewables over the last few years as a good area to invest?
Many PUCs are reluctant to allow too many coal plants to close due to local politics and fears about grid reliability.
You can look up articles. I found one from November saying he was on 128B, a second one in October saying 122B. So I guess between the two he liquidated 6B of investments.