For Question 1 and if i understand your question correctly, you had a carryover because you did not receive a full credit for your foreign taxes paid in 2019.
The way the credit works is that you can claim to the lesser of the amount of foreign taxes paid or the U.S. tax liability on the foreign income. So you can pay US taxes on the same income and still receive a Foreign tax Credit. You won't be able to claim the entire credit however because of the restrictions that i just mentioned thus this creates a carryover. This is because the Foreign taxes exceeded the US tax Liability and the FTC is limited by the US tax liability on the foreign income.
So in answer to your question, yes you can have a carryover even if you pay US and foreign taxes
For question 2, the carryover will expire in 2029.
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