Correct way to initialize HashMap and can HashMap hold different value types?

So I have two questions about HashMaps in Java:

1. What is the correct way to initialize a HashMap? I think it might be best in my situation to use:

   HashMap x = new HashMap();
   

   But Eclipse keeps suggesting that I use:

   HashMap<something, something> map = new HashMap();
   

   Which is better?

2. Can a HashMap hold different types of objects/data types as values? For example, would this work and be OK:

   map.put("one", 1);
   map.put("two", {1, 2});
   map.put("three", "hello");
   

   In the first put(), I want an int as a value, in the second an int[], and third a string. Is this okay to do in Java with HashMaps? Also, is it okay to store a HashMap as a value within a HashMap?