First of all, I just want to know that I'm just a normal human being... 
Therefore, there's might be some flaws in my judgement... 
So, an early apology from me should compensate that...   
Now... 
On to the questions you had in your mind...   
1. Since Kotarou and Kagari are connected (mentioned in the Terra route), let's just assume wherever there's Kagari, Kotarou will be there...As for how Kotarou brought the five girls, I thought Kotarou used some of Kagari's theories and equations to bring them from the branch worlds...   
2. Esaka-san, maybe? Or Luis? Anyway, just think of anyone that Kotarou knew in his life to say that deep meaning about 'Youth'... 
    
3. Please specify your question...I'm sorry but I kinda confused on what you want to know...Do you want conformation about how Kotarou's fate in Terra route is different from the normal route? If you do, just think of the Terra route as another branch world from Kagari's newest theories and equations that has nothing to do with the other branch worlds...   
4. She just using the footnotes Kotarou's been doodling at the side of the Thesis, to uncover the ways to safe the planet.   
5. Well, I do think the conflict between Gaia and Guardian has ended seems to be a good memory for the Earth....