Clinton savors moment and 'a milestone'
The phrase "a milestone" is only enclosed in single quotes here to indicate that it is being quoted verbatim (in this case, quoting Clinton). The meaning of the sentence is simply "Clinton savors [the] moment and a milestone." (Articles are often dropped in headlinese.)
The second one is like titles, "Tom and a jacket" which can mean a story of tom and a jacket.Is it like that or a complete sentence?
Your assessment is correct. Headlines are sometimes just noun phrases and not complete sentences. This is basically the same as titles for stories (e.g. The Lion, the Witch, and the Wardrobe or Alice's Adventures in Wonderland).
India's Modi brings message of friendship to Washington -and a little humor.
Well that should be 'friendship in Washington'?
This question has nothing to do with headlinese. You always bring X to Y. To bring in implies that you are carrying the thing in a container, e.g. He brought the documents in a briefcase.