Chikyuu wa Boku ga Mawasu

1. did his childhood friend really die? or would he have managed to save him
I think realistically the friend died, one of the many events that the MC regrets, which pushes him to escape into his dreams and undo it. In real life, saving his friend didn't actually happen, but the MC has mentally grown and accepted the death kinda(?)
...or not...maybe the friend lived thanks to forewarning the MC got and he managed to save him?

 

2. the ending

i THINK that only a part of the ending scene was a dream and the rest was reality.

like, him greeting Natsu and his brother was real, him going to class and talking to his classmate (foreshadowing that he's able to make new friends now) was also real.

 

but then he falls asleep in class and "wakes up" and bumps into the dream eater- this part was not real, it was still him dreaming whilst sitting in his desk and taking a nap. the purpose of this new blank dream is probably to tackle his problems with deciding on a career, indicating that there will always be problems to solve in life, so he will always meet the dream eater again to help him.

I thought she couldn't exist outside of a dream, does it mean he's dreaming once again?