1. Not with double qoutes, but by changing the search keyword logic to “AND”: https://goo.gl/Cu5Egs
2. Make sure you have the Post Tags selected on the configuration of the keyword autocomplete source: https://i.imgur.com/rXWZp9r.png
If it does not show up, then the tags might be under a different taxonomy maybe.
3. Unfortunately that is not yet possible.
4. On the General Options -> Ordering panel: https://i.imgur.com/3cXXBnq.pngBest,
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