How to translate 冲 in a phrase 道冲。 Is there any meaning of the character 冲 that allows to translate it as Vessel (or empty vessel)? The section four of 道德经 states: "道沖而用之或不盈" - 冲 is usually translated here as an empty vessel or emptiness of a vessel - but I am not sure what is the basis for such translation.
There is no original meaning of 沖 that means "vessel" or "pour into". "Pour against" as a later extension, maybe...

说文 is pretty clear that 沖 means to "surge up and shake extensively", i.e. to "gush" (of water).

There is also this phrase in pre-Han text: "盈而不沖". "Fill up but not gush".

Supposedly, there are two original versions of the passage in question:

帛書甲本：□□□□□□□盈也，潚呵始萬物之宗。銼其解其紛，和其□，同□□□□□或存，吾不知□子也，象帝之先。 

帛書乙本：道沖而用之有弗盈也，潚呵似萬物之宗。銼其兌，解其芬，和其光，同其塵，湛呵似或存。吾不知其誰之子也，象帝之先。

Your quote is already a slightly edited paraphrase. If we are to stay faithful to what is literally written, we may translate:

道沖而用之有弗盈也，潚呵似萬物之宗 ... 湛呵似或存 = The Law gushes and administers whatever is not filled up, a deep reservoir as if the source of all things ... a flood as if something is alive.