Is jQuery a DSL?

Sorry but there is no any rule that says if this is a DSL or not.

• A way jQuery wraps a DOM access syntax into $('div -id') is  DSL.

jQuery is an internal DSL.

A lot of other frameworks could be labeled DSLs if we go down that path. The way jQuery wraps DOM access syntax into $('div-id') is DSLy.

Yes As it is small languages, focused on a particular aspect of a software system

We can consider JQuery as a DSL but actually its not  DSL.

jQuery is a fairly typical example of an internal DSL. An internal DSL uses the syntax of its "host" language to provide an API that feels like a DSL.

No.
jQuery is a JavaScript library conforming to the syntax of the language, with a selector engine compliant to a high degree with CSS selectors.

Yes - jQuery can be labeled as DSL.

JQuery is a typical example of an internal DSL and there is no any rule that says if this is DSL or not.

A lot of other frameworks could be labeled DSLs if we go down that path.
The way jQuery wraps DOM access syntax into $('div-id') is DSLy.
http://www.quora.com/Is-jQuery-a-DSL/answer/Vilan-Natanzon