Question #1: Yes, it should be an increase to the cost basis.
Question #2: You will go to the specific sales in question and make an adjustment to the cost basis manually for each transaction where you need to adjust it.
This is a very common action because the brokerages do not always know the full cost basis of your holdings. It's the reason it's so important for you to retain your detailed records for buys and sells of your investments.
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