I am wondering if a Miner can spend the amount mentioned in a data-insertion transaction for herself? And what is the incentive for Miners to confirm data-insertion transactions?
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By data-insertion transactions you mean OP_RETURN outputs?
Typically those outputs have amount 0, so there is nothing to spend. But if the amount is not 0, those coins are burnt, and nothing - even miners - can change that.
However, such transactions can (and almost certainly, will) carry a transaction fee like every other type of transaction. That fee goes to the miner who includes the transaction in a block, and is the incentive to do so. This is the same for every type of transaction.