The difference between "few" and "a few" is: "few" means so little that it's a problem while "a few" just means a small number. E.g. "Poor thing she has few friends." but "She has lots of problems but fortunately she has a few friends." In addition, "few" doesn't collocate with "only". Grammar is strange. Ask me I try to teach these details. Hope this has helped otherwise you can flunk me.
"We remained only few days" sounds like incorrect English to me. I can't really explain why you need the article, but...
When you use 'only', it kind of turns 'a few' into 'few' implicitly. E.g. "it was only a few dollars" means it was less than you were expecting, so the meaning of the original Italian is preserved.
It seems both are correct, have a different meaning, so that a variant without article is a lot more rare e.g.: We have a party tonight? but we have only a few beers - meaning, we will drink beer tonight.
We have a party tonight? but we have only few beers - meaning, some of us, lucky devils, would drink beer tonight.