select a JSON element which have no node name

Question 1

Using . you can get the current element. There is no possibility using JsonPath to extract key names. Hence, you can do this in JavaScript by using for and grabbing the key name.

The following HTML shows a complete example:

<html>

  <head>
    <link rel="stylesheet" href="style.css">
    <script src="jsonpath.js"></script>    
  </head>

  <body>
    <h1 id="h1"></h1>
    <script type="text/javascript">
      var o = {"q0":{"query":"WilLIAM","limit":3}};
      var key;
      for(var i in jsonPath(o, ".")[0]) key = i;
      document.getElementById("h1").appendChild(document.createTextNode(
        key
        ));
    </script>
  </body>

</html>

Here is a Plunkr: http://plnkr.co/edit/CaZD1lVhr1E2S8VN5vnP

Question 2

The documentation at http://goessner.net/articles/JsonPath/ would point to $.q0.

Question 3

By using Google's Gson library you can read as below.

HashMap<String, JsonElement> myMap = new Gson().fromJson(jsonString, new TypeToken<HashMap<String, JsonElement>>(){}.getType());

String id = null, query = null;
int limit = 0;

for (Entry<String, JsonElement> entry : myMap.entrySet()) {
  id = entry.getKey();
  if(entry.getValue() != null) {
    JsonElement je = entry.getValue();
    if(je.isJsonObject()) {
      JsonObject jo = je.getAsJsonObject();
      query = jo.get("query").getAsString();
      limit = jo.get("limit").getAsInt();
    }
  }
}
print("id : " + id + " query : " + query + " limit : " + limit);

Question 4

Acutally, you can use XPath on your JSON structure using DefiantJS. This library extends the global object JSON with the method "search" - with which you can query JSON structure with XPath. The method returns the matches as an array.

var data = [
       {
          "q0": {
             "query": "William",
             "limit": 3
          }
       },
       {
          "q1": {
             "query": "Joe",
             "limit": 1
          }
       },
       {
          "q1": {
             "query": "Bill",
             "limit": 2
          }
       }
    ],
    found_1 = JSON.search(data, "//*[limit=3]"),
    found_2 = JSON.search(data, "//*[limit>1]");

document.getElementById('output_1').innerHTML = found_1[0].query;
document.getElementById('output_2').innerHTML = found_2[0].length;

To see this in action, check out this fiddle; http://jsfiddle.net/hbi99/zWU6x/

Also, check out the XPath Evaluator here to see and test XPath queries; http://defiantjs.com/#xpath_evaluator