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They could, for example, use the actual financial aid offer to try to reverse engineer each other’s finances.
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Possibly. Certainly if custodial parent has an EFC of 0 and no assets, but CSS Profile comes back saying that the family will be “full pay” it certainly lets the CP know that the other side has a strong financial situation.
I think some CSS schools actually split-out the contribution. So if Household 1 has an income $80k (minimal assets) and is told that they need to pay $10, and Household 2 is told that they have to pay $25k, it wouldn’t be hard to estimate their situation.