'In a couple days' is not correct. We say 'in a couple of days' . 'Couple' can mean two or a few. Although when we talk about days, weeks or months etc we normally mean more or less two, 'couple' is often used to mean just a few. 'Can you loan me a couple of dollars?' does not mean exactly two dollars it means a few dollars.

In short: yes. ;-) Technically, I think the 2nd one is right, there has to be an "of" in front of "days", but in daily conversation everyone will know what you mean anyways.

"In a couple of days" is correct. 'In couple of days' is grammatically incorrect. "a couple of" is together an expression that means ' a combination of 2' or 'a pair of'.

should be "in a couple of days" some say "in a couple days" but I don't believe it is correct English. It's like people reply to you saying "I am good" to the question of "how are you?" this is bad English but it is so widely spoken (" I am speaking what I hear in America, ...)

'In a couple of days" is the better way to say that but, yes, they mean the same thing.