Is not null:

db.mycollection.find({"IMAGE URL":{$exists:true}});
db.mycollection.find({"IMAGE URL":{$ne:null}});

Between dates:

db.getCollection('tournament').find({"start_at": { $gte: ISODate("2015-06-24T00:00:00.000Z"), $lt: ISODate("2015-06-29T00:00:00.000Z")}})