Is it necessary to give a "source" for something while answering on ELU which we are getting it from some website but rewording it or typing it without looking at the material. For example: Doltish - someone who is foolish. But I looked it up in the online Websters Dictionary. So in writings like these should I still give a reference or source?
There are two excellent reasons for providing a source:
To give credit where credit is due. You have an ethical obligation to your source, no matter that you are paraphrasing or quoting from memory. Moreover, in many situations you have a legal obligation to your source. For instance, people who post content from ELU or any other SE site are required by the Terms of Service to post a link to the original question.
To lend authority to your answer. You and I are merely anonymous posters, with no credibility other than that provided by our reputations here. But a citation from an established source like Merriam-Webster, with a long-standing international reputation, carries great weight.
As far as I know, there is no legitimate countervailing reason not to provide your source.