Yes, the earth being round was common knowledge (notion goes back to Pythagoras, and it's pretty obvious if you've spent any time on the ocean). The circumference was at least somewhat known but Columbus was off by about half. The most plausible theory is a mapmaker Columbus believed was off.

The earth's' circumference was first calculated by Eratosthenes of Alexandria by figuring the angular difference in 'vertical' between the two points. Given the known angular difference and known distance between the two points he could then find the circumference based on the curve of that segment. There’s some disagreement over how close he came to the actual distance based on what we consider to be a ‘stadia’, but if you use the same stadia conversion for the distance between the two points as for circumference, he’s close (excepting the planet isn’t a sphere but an oblate).

Anyway, navigators who knew the actual circumference would not attempt the trip as the then-most-modern blue-water vessel, the carvel, could not go that far and also carry enough food/water for even a minimal sized crew.

Personally, I think Isabella gave him money for the trip as it was a win-win for her. Columbus was a bit of a PITA, so this would either get rid of him, or get access to spices, which were particularly expensive in the Iberian Peninsula as they were far from the Western terminus of the Silk Road.