key: {$exists: false} / key: {$type: 10} / key: null quering gives inconsistent and unpredictable behaviour, so to workraound needed to implement querying of this kind of parameters

shell script example:
db.testcollection.ensureIndex(

{date: -1, country_code: 1, user_id: 1}

,

{unique: 1, background: 1}

);
db.testcollection.insert(

{ date: new Date("08/27/2010"), tot_visit: 100}

);
db.testcollection.insert(

{ date: new Date("08/27/2010"), country_code: "IT", tot_visit: 77}

);
db.testcollection.insert(

{ date: new Date("08/27/2010"), country_code: "ES", tot_visit: 23}

);
db.testcollection.insert(

{ date: new Date("08/27/2010"), country_code: "ES", user_id: "and...@spacca.org", tot_visit: 11}

);
db.testcollection.insert(

{ date: new Date("08/27/2010"), country_code: "ES", user_id: "andrea.spa...@gmail.com", tot_visit: 5}

);
db.testcollection.insert(

{ date: new Date("08/27/2010"), country_code: "ES", user_id: "andrea.spa...@progloedizioni.com", tot_visit: 7}

);

db.testcollection.find(

{date: new Date("08/27/2010")}

).count(); // 6 [OK]
db.testcollection.find({date: new Date("08/27/2010"), country_code: {$exists: true}}).count(); // 5 [OK]
db.testcollection.find({date: new Date("08/27/2010"), country_code: {$exists: false}}).count(); // 1 [OK]
db.testcollection.find({date: new Date("08/27/2010"), country_code: {$type: 10}}).count(); // 1 [OK]
db.testcollection.find(

{date: new Date("08/27/2010"), country_code: null}

).count(); // 1 [OK]
db.testcollection.find({date: new Date("08/27/2010"), country_code: {$exists: true}, user_id: {$exists: true}}).count(); // 3 [OK]
db.testcollection.find({date: new Date("08/27/2010"), country_code: {$exists: true}, user_id: {$exists: false}}).count(); // 2 [OK]
db.testcollection.find({date: new Date("08/27/2010"), country_code: {$exists: true}, user_id: {$type: 10}}).count(); // 0 [??]
db.testcollection.find({date: new Date("08/27/2010"), country_code: {$exists: true}, user_id: null}).count(); // 2 [OK]

changing the order of key querying or indexing produces slightly different results, always bogus