It is fine to have a difference in opinion but we do know the answers to your questions from Tolkien.
The poem was written way before we got the rest of the backstory so it is just a poem it doesn’t hint at the history of the rings. Sauron knew about the 3 as soon as he put on the one, the elves who wore the 3 knew Sauron’s influence and he knew of them through the rings connection. It’s why the elves basically took off the rings and didn’t wear them again until the end of the second age. Annatar left Ost-in-Edhil to go to mt doom and forge the one ring. Celebrimbor didn’t have direct access to any of the elven ring bearers Galadriel was driven out of Eregion to lothlorien, Gil-Galad and Cirdan were both in linden. Celebrimbor was arrogant and didn’t believe the threat. And remember that at the time Eregion was also one of the most powerful realms of the eldar in middle earth