Spoilers, Sweetie…
The obvious answer is “Yes, the suit contained young River, and so young River killed the Doctor in the suit.” And River “missed” because she could not kill her younger self (and her “of course” quote is because she realizes/remembers her killing the Doctor as a child).
But…
That’s an “on the nose”, TOO obvious answer. Stephen Moffat tends to not only avoid the obvious, but to subvert it for dramatic purposes. My opinion?
The person in the Astronaut suit? Well, it’s The Doctor, of course.
Who with the what now? The Doctor killed himself? Why???
Because he had to. The Doctor knows that he has to make sure that River’s timeline “works” because like his her life is a “fixed” moment in time. He can’t “break” that timeline and in that timeline he is killed by River. So…
He frames her.
Yup, he kills himself, by using… himself. Now, of course, The Doctor being… well, The Doctor, he of course has a way out of all this.
Maybe the magic moment when someone asks the Ultimate Question:
“Doctor Who?”