From this site and others. They started making it directly after the second game. It's common knowledge.
Only in your dreams.
It was in fact the opposite as Nomura himself stated more than often until 2012 to not expect KH III at all.
They didn't start to truly work on KH III until 2012 (planning stage) and it was announced only in 2013.
There are no official statements that say otherwise so this "common knowledge" is nothing but unfounded fanwank and clickbait.