To which extent can I expect German-speakers to understand Sütterlinschrift? In which of the following situations would it be fine to use it?
Actually, I would never expect anyone to understand Sütterlin, independent of the situations you describe. There are exceptions, of course, and within the older age group, you may actually find people to read it easily. My grandparents learnt Sütterlin in school, while my parents did not. Me neither, of course.
To answer your question, you should only use it if you are sure the addressed person not only understands Sütterlin, but wants to read it. This restricts the use to some personal settings and communication with linguists, basically.
As OregonGhost wrote, Sütterlin is completely out-of use in Germany, and I would expect people to be able to read Sütterlin only in special areas, for example archives or libraries (old library catalogues are partly written by hand using Sütterlin). Using Sütterlin in written exams nowadays would be a certain way to annoy the examiner severely...
None of these situations would be appropriate if your friend does not share your language interests (regardless of age).
A late answer, I just now found the question.
Despite what the others said, we were actually told by several teachers at high school that Sütterlin is still strictly speaking accepted when handing in a test or homework (as in, the teacher has to accept it, and pretty much regardless of the subject). I’m not entirely sure if this is actually true but since several teachers told us this, I, being a smart-ass, obviously had to try this claim. It worked.
For context, I went to school in the 90s. And yes, I learned Sütterlin in elementary school but at high school I was one of the only ones who had.
Not attempting to contradict any of the other answers, which in my humble opinion have nailed most of the issue, but none have addressed the question of companies and official forms.
A handwritten letter to a company in Sütterlin would be very weird. Unless you’re really 90+, learnt it at school and never used any other handwriting, the company would (as soon as it has figured out the meaning of the text, because they likely can’t read it) ask themselves what actually just happened. It’s anybody’s guess what they would think, but it’s not worth the trouble — especially since computers with printers are now widely available.
Not even bank transfer forms would qualify. My grandmother once tried to fill one in — frankly I never saw the form, just read on the account statement »50 Mark für Jan, 50 für Kalus, Rest unleserlich«. Yes, granted, she had pain in her fingers, but she likely also wrote in a very old-fashioned handwriting.
On official German forms (and likely Austrian and Swiss ones, too), Sütterlin would, in my opinion, have to be accepted. Reasoning: There are those people 90+ that have never used any other handwriting. It might take a little longer for the civil servant to read it, (see above) but they can’t really reject it.
However, if the official thinks you’re pulling their leg, things might change, and you might still be required to write it properly. Remember that Sütterlin hasn’t been taught as a handwriting for over 70 years.
I never saw Sütterlin before and could read it without any external help. There are only a handful of characters that are really hard (S being the worst) 
, but if you read the whole sentence you will know what it means.
The handwriting I saw was a very clean one. Just like any other handwriting it really depends on the writer.
If you write me a letter in Sütterlin or apply for a job at my company (which I don’t have) … go on! You get the job!
I was born in 1969: we never had that stuff at school.
Written exam in German - not unless it were an analysis of historical handwriting forms or something.
Written exam in physics - God, no.
Residence application and other offical forms - nope.
Letter to a company - only if it's the "Bund für deutsche Schrift und Sprache"
Postcard to a friend, <30 years old - no. Plus, no one under 30 sends postcards anymore. And Facebook and Twitter don't use Sütterlin.
Postcard to a friend, >50 years old - how about >80? Viele Grüße aus der Weimarer Republik...
