Money and wealth are two different things. Money is an item that can be used as a store of wealth and as a convenient medium of exchange, but it's not the same thing as wealth. If you have a lot of money, then you have a lot of wealth. But you can have a lot of wealth (in the form of, for example, real estate, company ownership, financial assets and loans, and physical capital) and not have a lot of money.
There is a very, very large amount of money in the world, so bitcoin would have to appreciate in an extreme way in order to replace the other forms of money. In that case someone owning a lot of bitcoin will be pretty rich. But having half the world's money is a much smaller thing than having half the world's wealth.
Your inflation question isn't real clear to me. Because bitcoin is not kept in banks and lent out, a bitcoin user in your proposed world creates inflation when they spend their bitcoins, increasing demand for goods and services. This increased demand drives up the price of those goods and services. Prices react pretty quickly, so it seems like the effect of an increase in the effective money supply (the bitcoins actually being used, rather than hoarded) would have a similar effect when spent quickly as slowly. Think of it this way: if you are buying 1,000,000,000 toasters the first few thousand could be had cheaply at Walmart and Amazon. Then you would have to go to more and more expensive sources to get them. Eventually you would run out of sources and have to have them special made at yet higher expense. It's not the time that raised the prices but the actual purchasing behavior. Same thing is true of houses, yachts, islands, or whatever else a very rich hypothetical person might buy.