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I would guess that a conure and a tiel couldn't actually produce offspring. They're from different continents so genetically they're probably too different from each other. As far as I know all the hybrids involve birds from the same continent, and usually not too far apart from each other on the family tree.
As for the female tiel mounting the male, well, who says it always has to be "missionary position"? Rules are made to be broken, and it seems to me that this could lead to offspring if they're doing a good enough job of getting their vents together.
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