I'm not sure where you learned such a restricted use of "from."
If you follow this link and look at the definitions and sample uses of "from," you'll see that it's really quite a flexible word.http://www.merriam-webster.com/dictionary/from
"The store from Walmart" doesn't work at all (that's not a product from a brand/company). Actually, we wouldn't normally say "the Walmart store" either -- we'd just say "Walmart."
Either of these two works:
a) I went to Walmart to buy a new vacuum cleaner from Siemes.
b) I went to Walmart to buy a new Siemes vacuum cleaner.
In example 2, both work in theory, but a) is bad style with the piled up "from."
Both a and b in example 3 are fine.
I'm not sure I understand your comments about 3, though. The distinction I think you're trying to make between brand, producer and origin would really be quite irrelevant in most cases -- but what do you mean by "though not otherwise".
It might be more helpful if you would write your comments/questions about the text in German. Expressing yourself in your native language is pretty much the norm here.