Is it normal to feel like I bought my way into graduate school after being rejected and then accepted when I was awarded an external fellowship?

From what I've heard the NSF fellowship is not an easy one to get, and having one seems to carry some sort of prestige. Sure, the program may have accepted you on the ground that they don't have to pay you, but the fact that you have an NSF fellowship may have changed the admission committee's perception of your ability, which could be what tipped the balance in your favour. No matter what, there is no point in dwelling on the past. What matters is how you perform in the program now, not how you got in. Don't be the college freshman who keeps talking about his high school athletic achievement; truth be told, nobody cares.

As for your lack of passion for the subject, I want to point out that passion usually does not precede mastery of a subject. Rather, people usually develop passion after they become good at something. So I don't really think lacking passion at this point is a deal breaker. I'm sure astrophysics is large enough for you to find something that you are good at and can develop a passion for. Of course, if you can't see yourself doing research, teaching, or anything science-related in the future, you might want to rethink about your decision to go to graduate school in the first place.

First, congratulations on doubting yourself. That you doubt yourself will make you a better researcher. You will check your findings and take more care in your work. A little self-doubt is important in the world of research. Alas, it is a weakness in the world of promoting your research, so there is certainly a balance.

Second, congratulations on the NSF Award! That is very prestigious! Consider that the NSF Panel which reviewed these awards had more information about you and more time to consider each specific application than members of the admissions committee. They literally made a more informed decision. And that decision did then influence the admissions committee to update its own decision.

And yes funding matters. You did not buy your way into graduate school. You earned your way into graduate school. Getting a NSF Award is the hard way.

Yet while funding does matter, no one will take a "free" student they are not interested in. Every PhD student is a significant commitment in terms of time if nothing else. Graduating doctoral students is the core of what we do, and why many of us are professors. They would not have admitted you if they did not expect to want to work with you. You made it possible for the school to afford to admit you.

In every admissions committee I have ever worked on any serious application is read by at least one committee member. That committee member then makes a recommendation for further review, so some applications are reviewed by only one faculty member. In my experience nearly completed doctoral application is see by at least one faculty member. Unreviewed cut-offs for test scores alone may actually occur, but I have not seen it. It is, at most, quite rare. So it is likely you were reviewed by multiple faculty members, put on an alternate list, and then everyone else they asked did accept. Then when your funding came through, acceptance was possible.

You will find your passion. Did you know that the current lead of the Office of Science and Technology Policy, John Holdren, started in astrophysics? He was a lead in the Paris Climate Accords. And stop calling it "space physics". Sec. of Defense Ashton Carter, who just appointed the first openly gay Sec of the Army, started as a physicist. Physics is your five year plan.

If you look at my cv I started as a Math/EE in a nuclear plant, went into computer generated holography, wrote my dissertation on the then-imaginary idea of Internet commerce, worked at Sandia Labs in CS, moved to Kennedy School of Gov, then moved to an Info/School. I probably have at least one career left. You will find your passion.

There are plenty of people who would feel like that, especially when they are young and insecure. I'm not a psychologist, but I think it's some kind of manifestation of the imposter syndrome. When I got admitted into graduate school, I was coming after 2 years of inactivity and I was sure I'd get kicked out in one semester. At the end of that semester, I had passed my qualifying exam. Then, I was sure no one would hire me after graduation. In the end, I got 5 postdoc offers, one from each place I had applied to.

The fact is, your admission committee had little to go on by just looking at your GRE scores, and it is possible they had other candidates with better scores and research experience. But, as a faculty, I'd view your NSF fellowship as a better predictor of your future performance in the graduate program, especially if your undergraduate research contributed to obtaining it. Besides, I know personally people with poor GRE scores that are full professors at US universities now. I think a good GRE score predicts better how you would do in your graduate classes, than in research. But, however nice is to get high scores on the exams, no one will ask you about them after graduation.

As you will get more confident with what you can do as a researcher, you'll probably stop asking yourself the question if you are "good enough". You'll just focus on doing quality research work, and leave those doubts to your referees.