about något, it is more common to pronunce it as it is written, or as "nåt" ?
Either works and no one will think twice about the one you used. However if Swedes for some reason want to sound as formal/clear as possible, perhaps when talking to an elderly person or learners of Swedish, we might pronounce the whole word.
Why is"do you need to shop for anything" unacceptable?
"Köpa" is buy. "Shop for" is "handla". "Behöver du handla något" = "do you need to shop for (go shopping for) anything?"