I have couple of questions trying to understand how BTC ETF works. I kind of know what is ETF and how it works in traditional markets.

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?

Shares of ETFs are bought and sold at market price (not NAV) and are not individually redeemed from the fund. Any applicable brokerage commissions will reduce returns. Beginning August 10, 2020, market price returns for BlackRock and iShares ETFs are calculated using the closing price and account for distributions from the fund. Prior to August 10, 2020, market price returns for BlackRock and iShares ETFs were calculated using the midpoint price and accounted for distributions from the fund. The midpoint is the average of the bid/ask prices at 4:00 PM ET (when NAV is normally determined for most ETFs). The returns shown do not represent the returns you would receive if you traded shares at other times.

2. Why it is called iShares Bitcoin Trust? Does the word "Trust" mean anything in this case?

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?
 

Notably, MicroStrategy still holds far less than the 474,627 bitcoin held as of yesterday by BlackRock's iShares Bitcoin Trust (IBIT), which is the largest bitcoin exchange-traded fund (ETF).
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BlackRock. "iShares Bitcoin Trust."

Is there correlation between the price of IBIT and number of BTC's they have?