why is an article 'a' needed here, what is the indication for it in the Swedish sentence?
You don't need an indication, it is grammatically in correct not to use 'a' in English.
I can never remember what a "duvet" is.
Can someone tell me how to translate "täcke" to American English?
I would say, "I am sleeping without covers." Duvet is an uncommon term here in North Eastern US. It is newly introduced, (1980s? via marketing), and a bit pretentious. "blankets", or "covers" are the common terms.
I think a duvet is more like a fluffy quilt, or a down comforter, but used without a top sheet.
Here's a UK explanation for if it's useful...... - duvet - most people use these now. It's a padded fluffy bed cover which keeps you warm. You buy a duvet that's the same size as your bed, and they come in different grades, from a small amount of warmth to extremely warm. They are filled with either down/feathers or with a synthetic filling. You always buy a duvet cover and this can be any colour or design, usually bought as a set with two pillow cases. A duvet cover is like two sheets sewn together, and you take it off the duvet to wash it. - quilt - is sort of old fasioned, but still used, usually with a sheet underneath (you wash the sheet but not the quilt). A quilt is padded and is there to give warmth. It doesn't have a cover and is often very beautiful, like for example a patchwork quilt.
it should be "Jag sover utan en täcke" right? since the translation says its "a quilt".
In Swedish, it's more idiomatic to leave the indefinite article out. (Also, it's "ett täcke")