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@pinguino I'm traveling, so may not be able to respond if you have follow-up questions, but wanted to offer a couple comments:

• The partnership is using average cost because of IRS Reg 84-53, which says "IRS Revenue Ruling 84-53 provides that a partner has a single unified basis in their Partnership interest".  That means that picking which lots to sell to manage losses doesn't work.  You may be able to find a tax advisor who will give you a rationale for ignoring this, but that's why the sales schedule will use average cost.
• Your broker should not be reporting cost basis on the 1099-B.  They can't know it, because the cost basis changes with every K-1, and they don't see the K-1s.  The fact that they did just means that you'll report a different basis on your tax return (there are codes to allow you to correct what the broker supplied).  If the IRS ever asks, you'll have the K-1 to use as backup.  In the future, you should only be using your own records for cost basis.  The broker's will never be right.
• Because of unified basis, and any other adjustments that are made, partnerships are terrible vehicles for frequent trading and wash sales.  Figuring out how to factor the wash sale into the calculation is way outside this forum.  But when you figure it out, you'll probably be using a basis that differs from what the partnership provided.  That's OK.  You just need to keep good records and be prepared to justify them.
• If tracking all this seems like more than you want to take on, a possible answer is to just sell the entire position.  As long as your 2022 + 2023 tax returns combined match what the 2022 + 2023 K-1s report, you've solved the wash sale and broker discrepancies.  That's not investment advice:  just a practical way to solve these headaches.

On some of your other questions:

• Withdrawals and Distributions will equal the cost basis of any shares sold + any dividends that the fund sent out.
• Q3 & 4:  you've got it right
• Q5: As Mike said, all 0s and you avoid the duplication problem.  The only reason you wouldn't use all 0s is if the partnership distributed 'Ordinary Gain', which yours did not.

Hope that helps!

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