Also, assuming that a message is phishing is usually not harmful in any way. If I got an email from dropbox.com (and were a Dropbox customer), I'd ignore the email, and just type "dropbox.com" in my web browser to see what's up. If you're paranoid, you don't need to be super smart about what exactly is phishing.
This isn't a fair test.
And yes, I failed that question because I assumed that it's information that I was expecting. I don't open PDFs unless I am expecting it, because who wants to spend the time waiting for it to download and render for something that's likely spam?
And while pdfs can be attack vectors, they're not an especially strong one - it's not like running an exe with administrator privileges.
Comparatively giving a third party access to your emails should definitely raise flags.
I honestly think this should never be done because users shouldn't be expected to know which domains you do and don't own.
As to your second point, I agree in terms of 'best practices', but in terms of teaching about phishing, the fact is, companies do use multiple domains (and some deliverability guides actively encourage different domains for marketing emails and transactional emails - companies should use subdomains for this, but not all are that savvy).
Given that companies are sending from multiple domains, I think the litmus test for phishing is:
"Is the email trying to get me to give me information? E.g. a login on the wrong site, sending card details or anything like that"
Your pdf reader should allow you to open a pdf without being compromised (just as your browser should allow you to click a dodgy link without being compromised). So I think that item should pass the litmus test (unlike the email reading one).
If that blurb was meant to be taken as "You happen to know that your school only has a .edu domain", then yeah, this would have been conclusively phishing. Otherwise, just because it might be malicious doesn't mean it's phishing.
And PDFs are mostly harmless if you don't use Adobe Reader, since it's either a small attack vector or in a sandbox.