Do the ETF managers have no discretion in determining when to buy? I was under the impression that they usually handle these changes to indices gradually even under normal circumstances.

They do, but one performance metric for these ETFs is tracking error. So they want to try to match the index closely.

The operators of the fund are allowed to do whatever they outlined in the prospectus to track the index, some funds allow futures, options, and swaps along with equity shares to maintain parity with the index.

There are ways to gain exposure to a single stock without directly purchasing shares, options and swaps being the most common. Owning the actual shares makes things easy for the fund operators, but there are other ways.

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of course they do. read any prospectus for a FUND and funds track INDEXES using rules. inclusion in some index doesn't hamstring anyone.

blind purchases are not going to happen. people assume passive indexing is brainless, but it isnt.