I am a fan of always including null explicitly as that carries meaning.
While omitting a property leaves ambiguity.
As long as your protocol with the server is agreed upon any of the above can work, but if you pass nulls from the server I believe that makes your APIs more flexible later.
Should also mention that javascript's hasOwnProperty function gives you further insight.
/* if true object DOES contain the property with *some* value */
if( objectFromJSON.hasOwnProperty( "propertyName" ) )
/* if true object DOES contain the property and it has been set to null */
if( jsonObject.propertyName === null )
/* if true object either DOES NOT contain the property
OR
object DOES contain the property and it has been set to undefined */
if( jsonObject.propertyName === undefined )