Yes, the basis is the amount you contributed to the Roth IRA. If you recharacterized the $3,000 Roth contribution amount but only $2,500 gets transferred because of a loss you still made a $3,000 contribution and therefore have a $3,000 basis.
Yes in your example, your basis would be $9,000 (the recharacterized contribution amount, not the actual amount transferred to the traditional IRA from Roth IRA).
Yes, if you had a $9,000 basis and converted the full balance of the traditional IRA ($7,000 because of losses) then you will have a $2,000 basis to use up in future years (will be carried over to 2023).
@BUND
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