A formal organization is an organization with a fixed set of rules of intra-organization procedures and structures. They have a definite place in the organization due to a well-defined hierarchical structure that is inherent in any formal organization.
Yes, he still has Sage of the Six Paths chakra even without Kurama. Hagoromo gave him his chakra, he didn't give it to Kurama as he is another chakra. However, Naruto lost more power after losing Kurama since he was his primary source of power.
Naruto can touch the chakra rods thrown by momoshiki which can only be done if someone has six paths power. In Naruto the last , he goes into sage mode without any meditation which means he has six paths power.
No he has not lost the power according to what I have seen and Naruto Wiki page. Here is a little quote from the wiki page —-”Naruto's Six Paths Sage Mode cloak changed several times throughout his later years”. it says over the years so naruto definitely kept it.