Re: How did Obito knows that Kakashi Let Rin Die?
I am just putting a link to my thread in here because the answer to your questions is directly in the last manga pages I used. These two probably most important:
This answers a lot of the above quotes/posters. Kishi can of course come out and Plot-No-Jutsu us making this whole point irrelevant but this was only a couple of chapters ago and that is too close for even Kishi to contradict himself ;p
Obito says to Kakashi "...You let Rin die." not "...You killed Rin.". I am sure we will see next week Obito (I don't want to use the word obviously because when it comes to Kishi obvious is null and void, so instead I will use the word evidently...) evidently must see through the shared Sharingan or some other way why Kakashi had to kill Rin and/or if it was Kakashi who killed Rin (depends on what theory one is siding with) and like Deadai says above that would mean Kakashi had to have known Obito were alive/saw him/witnessed him, etc... Which as one can see from the 2nd linked page above, Kakashi 99.9999999% does not see Obito (once again unless Kishi does his thing) because look how freaking shocked Kakashi is that Obito knows Rin is dead AND on top of that does not even come outright to blame Kakashi (as Kakashi asks later in the same page why Obito isn't blaming him?).
Once again there is a huge difference between "...You let Rin die" and "...You killed Rin". First major difference is Obito obviously knows Kakashi didn't kill Rin or at least not in cold-blood, and Second major difference is by saying that Obito makes it clear the IMPORTANT thing is Kakashi broke his promise to protect Rin (which was a major reason Obito gave Kakashi his Sharingan as well if you go back to that chapter) and as we see Kakashi is shocked/flabbergasted/dumbfounded that not only does Obito know Rin is dead, but Obito clearly doesn't directly blame Kakashi for the death, scaring Kakashi even further because he is probably now realizing how many secrets Obito knows AKA Kakashi's entire life from Kannabi-Bridge and forward. (Think of all the times, even recently we have seen Kakashi upset, sad, and mourning how he couldn't keep his promise to Obito and/or save Rin, which is why as we see in the link I am going to put below that when Tobi said "Kakashi...you always open your mouth to easily...It's no wonder you've lived a life of regret.")
Which is why for about 2 or so chapters Naruto tries to get Kakashi to snap out of his depression, but I would guess that it is kind of hard when the person who saved your life and sacrificed theirs has now equated Kakashi's life as pure failure with a side order of whine-niken and french-cries ;p
P.S. - You cannot compare Tsunade to Rin ESPECIALLY as Medical-Shinobi's. I could possibly agree and/or see where you can theorize that a medical-shinobi has a better chance at delaying death, but I don't think Rin and Kakashi realize Obito is alive and Rin, after having the Sword of Zeus plunged into her heart, asks Kakashi to please remove his Chidori and give her and Obito a minute alone so she can explain why Kakashi just destroyed her chest cavity.