German is diverse are as many languages, but English and French are far more diverse.
My takeaway:
* Lots of people there (no offense intended if any CH people read this) referred to the language I know as 'written German'
* Lots of people (TV news guys are kind of the only counter examples) have a _heavy_ accent if they speak what they consider de_DE (Time for an anecdote: A good local CH friend of mine told me once that he talked with a DE guy for quite a while, on his best official German level, and was told all of a sudden if he can talk German (probably considered as 'accent-free') as well).
After fighting the 'everybody speaks German in CH/AT' a bit I'd like to point to the fact that there are lots of accents and dialects that just sound like gibberish if you're not used to them. Let's leave AT/CH out of this for a moment: If I visit the northern part of Germany/the shore, if I visit the most southern places, if I go to the southwest (Platt/Bayrisch/Hessisch) and people speak 'normally' I end up understanding 50%-70%. And I didn't even mention some dialects from the east of Germany.
Actually - if people from Berlin talk fast and use the local dialect, I'm lost..
I mean, why would people be blissfully unaware of the standard form.
Oh, and at least for Swiss German: It is kinda a different language (but extremely related to the written German): It's not just an accent with some funny words, but has a slightly different grammar, too. Most glarious is the lack of most of the verb tenses in Swiss German. So pupils have to learn quite some stuff to be really fluent in written German.
And even just within Switzerland there are dialects I don't understand (as in no clue what they're talking about). People speaking these usually switch to a more conformistic pronounciation when talking to people from other areas and don't use some of the more obscure words.
And for the reasons this all exists (at least for Switzerland): It's cultivated and all kinda part of your local/national identity. Politicians who speak a "too good" written German are deemed suspicious, almost all of the local culture (theater, local movies, even most of the Swiss tv produciton ...) is in Swiss German.
[Native Swiss German speaker, here.]
Switzerland is a very specific case, I guess. The level of national pride is very high, with a very prominent political party living close to the racism edge (and crossing it every now and then), protecting the country from outside influences (contractors from i.e. Germany are not really welcome there, often seen as stealing jobs).
Add to this national pride a good amount of _local_ awareness: CH is a federal system, each 'state'(Kanton) fighting for as much independence as possible. Heck, they don't even have a real capital city [1] because they don't want one state to surpass the others. Your local region of origin seems to be much more important there.
In addition CH has 4 (erm.. 3.5?) official languages and already some 'borders' that separate parts of the country into ~mostly french/german/italian regions. You drive 5 min and every sign switches from German to French and the whole culture changes (food, lifestyle are the easiest things to spot).
And of course those people will know some English, too.
The proper spelling is the least of your worries if you want to learn German.