What is correct: This process can take up to a few days. or This process can take up to few days (without 'a'). ?

but you can do this "in the next week, a few days maybe ( sentence continues)" "in a few days time, during the next week". I am not sure what this structure is called from an English language teaching perspective, that a linguist or a grammarian would use. I will try to find out to help you. It seems to be connected with the word next, and a time sequence. Next and a few being in a separate clause separated by a comma.

In this case, the answer is 'the next few days' . Examples when you might just use 'few days', without either 'the' or 'a' before it, are sentences like: There are few days in September when it doesn't rain. There are few people who would agree with you.

Yes, you can't say: In the next 'a few' days.... but In the next few days or over the next few days is correct. We can say a few or few in other situations. A few means little but positive, while few means little but usually with a negative meaning: I have few friends - small number in a negative way I have a few friends - small number in a positive way Hope this helps!

You will rarely say "few days" without "a" or "the" before it.