An ETF is effectively a company that does nothing but own bitcoins, so the value of a share depends solely of the value of the bitcoins owned by the company. For example, imagine that an ETF owns 1000 BTC worth a total of $97,000,000 and there are 1,830,200 shares. That means that each share is worth $53.
1. Where does IBIT price come from? Today it is around $53, however, BTC is about 97k already. I guess there is no direct correlation?
The value of a share is the value of the ETF / number of shares. The vale of an ETF is the value of the assets it owns.
2. Why it is called iShares Bitcoin Trust? Does the word "Trust" mean anything in this case?
A "trust" is a special legal entity.
3. What is the idea behind the BTC ETF? My assumption is Blackrock will sell IBIT shares, and buy BTC from the market for the money they've earned. If this is correct, do we know how much BTC they have bought? Where they kept it? Is there correlation between the price of IBIT and number of BTC's they have?
A ETF will take a deposit of money, buy bitcoins with it, and give the depositor the equivalent number of newly created shares. Or it will take a deposit of shares, sell the equivalent number of bitcoins, and give the proceeds to the depositor. The bitcoins owned by an ETF are held by a "custodian". CoinBase is the custodian for most ETFs.