Save json string to client pc (using HTML5 API)

You can use a Blob and the HTML5 a[download] feature to provide a JSON backup download:

var data = {a:1, b:2, c:3};
var json = JSON.stringify(data);
var blob = new Blob([json], {type: "application/json"});
var url  = URL.createObjectURL(blob);

var a = document.createElement('a');
a.download    = "backup.json";
a.href        = url;
a.textContent = "Download backup.json";

Here is a jsfiddle example: http://jsfiddle.net/potatosalad/yuM2N/

Yes, you can. This assumes that you have the json in text:

var toDownload=new Blob([text],{type:'x-whatever/x-backup'});
var link=window.URL.createObjectURL(toDownload);
window.location=link;

that is untested, but it should work.

You can use FileSaver.js.

Sample code:

//include the js file in html.
<script src="FileSaver.min.js"></script>    

// other code ...

//use it here.
var myjson= "{a:3, b:4}";
var blob = new Blob([myjson], {type: "application/json"});

var saveAs = window.saveAs;
saveAs(blob, "my_outfile.json");

Use JSON.stringify to create a string from JSON.

Fiddle: https://jsfiddle.net/9w9ofec4/3/