Mito, Karin, Nagato, and now Naruto have all Sensing. Two of them are not Jinchuriki, and one of the jinchuriki wasn't said to be perfect. Why the difference. I believe if Mito was a perfect Jinchuriki, Kushina wouldn't have problem with Kurama.
I am also expecting any of the shinobi alliance to go yellow flash, super sensor, etc.
---- As for now ---
In my opinion, Naruto never get a chance to distinguish his own power from Kyuubi's. The first time Naruto healed was on his way to confront Zabuza. At that time, there was no collaboration between him and Kyuubi. I have many thread on some forum dealing with this fact: Kyuubi started to eat Naruto's chakra since he was baby. So whose chakra does Kyuubi really have? He ate Mito's, Kushina's and now Naruto's. My guess is all these power Naruto has are Uzumaki power, and Kishi had to explain because we have non-jin Uzumaki with the same power.
Moreover, I am waiting to see Naruto in Goku's chakra. He is going to be awesome again, then, we will see that everything is from Naruto. Kurama is only giving power source.
Not only you are wrong, you are incredibly wrong:
The exchange happens only and only when Naruto starts using Chakra Mode, as Hachibi explained.
Not only that, but Yondaime's seal was made so only a tiny bit of Kyuubi's chakra would leak, and it would kinda defeat the purpose if Yondaime would let the Kyuubi stole the chakra of his son, expecially when he was a baby, right?
And considering neither Kushina nor Mito were perfect Jinchuurikis, Kyuubi didn't steal a thing
I do think Nagato himself could sense, considering Madara and Tobi aren't able to sense even with Rinnegan. Doesn't look like a RInnegan thing, but more the ability of the shinobi him/herself. Naruto getting Rinnegan wouldn't make him able to sense. I'm pretty sure Kyuubi or Sage Mode isn't enhancing his abilities like healing and sensing, but giving him new abilities. It'd make sense.
We've seen the Hachibi's chakra heal Kirabi, in his fight with Sasuke, healing the hit from Chidori and later his burnt away skin. On the otherhand, we've never seen a Bijuu heal damage to themselves. And Naruto got a variation because he used a special sealing technique. Naruto's own traits had nothing to do with it, else it would have happen long before.
And only Naruto and Mito possess the ability to sense hatred, instead of the regular chakra sensory that everyone else holds, including Karin.
Kabuto just says he got it from her, before going on to mention the Uzumaki clan having a strong life force. Nothing about the entire clan possessing regeneration, which fits with what we have seen.
However, the fact that Kabuto used to the Uzumaki Clan's exceptional Life Force essentially to explain where Karin's healing powers came from DOES imply a connection. The only unrelated bit of information he gave was that the Uzumaki all have red hair, which I feel was in part Kishi justifying the "big reveal" that Karin is an Uzumaki. However, it's pretty clear the Life Force is the reason for automated regeneration. I'm not saying everyone would get the same results as Kabuto, since his body can also liquify, but it stands to reason Karin could be an abnormally fast healer.
It can't be, because aside from Karin, we've never seen any such regeneration. Both Nagato and Naruto have been shown heavily wounded, Naruto was shown not being able to heal without the Kyuubi's chakra, and Tsunade had to create a whole specialized technique in order to gain such regeneration. Heck, we even saw Kushina bleeding without any sign of healing going on. The strong life force allows them to live longer then a nomal person, but there's not a single sign that it grants them the ability of regeneration.
However, good catch pointing out Yamato's technique. While Yamato needed seals to perform it (unlike Hashirama's alleged healing jutsu), it certainly could be proof that Hashirama's healing is pretty much straight-up Mokuton. I hadn't really considered that panel.
I still think Hashirama's jutsu is more indicative of his incredible Senju/Uzumaki Life Force, which is what grants his Mokuton all of its unique properties; it's not the wood itself that is amazing, it's Hashirama's chakra that can use the wood as a conduit. That's why strapping his face on your arm lets you wield 10 transplanted Sharingan, or why having his genes gives Obito/Madara the power to link with the Mazou. I also believe it's why his healing techniques are so incredible.
I think a Senju/Uzumaki could do the same things as Hashirama with an element other than Mokuton if they had the same level of power; if Tobirama had been as much of a badass, he could have probably just used his water, but for whatever reason his chakra must have been inferior, because you don't see people transplanting his genes for stamina.
It's a shame that Kishi has created so many overpowered Uchiha characters with unique eyes and powers that follow the theme of Yin/Spiritual Energies, etc, but only one dominant Senju character to represent Yang/Physical Energies. While Nagato/Naruto are chakra beasts and can handle the Rinnegan/Kyuubi, etc, it's hard to distinguish their own powers from those "borrowed" powers. Hashirama didn't need the Kyuubi to be a badass, he was badass enough to control the Kyuubi. He didn't need the Rinnegan, he was a necessary component for Madara to even awaken the Rinnegan... I wish we got more answers about the mysterious Senju clan and why we don't see any of them.