1. I think it was just known that he was fiercely loyal to The Godfather and had to be taken out pre-emptively.
2. They were just trying to shake any tails and keep Michael on his back foot by not giving him any more information than necessary.
3. Vito was a top tier strategist and correctly determined that Tattaglia couldn't have come up with so effective a plan, and Barzini's actions at the treaty showed to the discerning eye that he benefited most from both the actions before the treaty and the treaty itself.
4. Moe was probably overstating the impact on customer service.