I don't think that it's an "easy" feat to invent the Rasengan from nothing. Additionally, I don't think that even if Takumi had invented it, the village would reward him with the Flying Thunder God Jutsu as it is firstly probably stored in the Senju library, secondly requires a high-level clearance and lastly uses too much Chakra, therefore, making it useless to Takumi anyways as he's still a kid with only above average Chakra reserves. But future Takumi should have enough Chakra reserves to use it, so I think that learning it would be quite "handy" for more than a couple of situations.

Unfortunately, I'm quite busy with RL so the next chapter's update was significantly delayed. However, I've already written a good amount of the chapter and I'm going to have more free time for the next couple of days. So fingers crossed and let's hope that it will be soon be uploaded.

Yes, it's still being written. Takumi knows of Uzushiogakure's canon fate so he's going to try to change it but only time will tell if he can succeed.

Thanks for the comment! But who is Ushio? And isn't the reason for the destruction of Uzushiogakure not confirmed/known?

We will see how the plot goes.

Yeah, you're right but I think he truly took off when he was under Hiruzen

Well, the range of each byakugan is unique so maybe he can't see the target? (author starts sweating instesnively)

Well, he is an orphan so he shouldn't have any training in Ninja-related activities. As a result, Tsunade is likely to be better than him at least until they train under the third Hokage.