MongoDB - AND request on array with GeoJSON element

I've looked at other issues without finding a suitable answer for my problem, so I hope you may help me.

SITUATION
I am currently working on a localisation app with MongoDB. For the moment I test my queries in the MongoDB shell.
I have a collection of Point documents with locations. I use GeoJSON objects for the coordinates of my point.

Here is what a Point document looks like :

{  
    _id: "Roma_DellArte",  
    localisations: [  
        { location_type_id: 1, location: { type: "Point", coordinates: [ 41.9097306,12.2558141 ] } }  
    ]  
}

My location_type_id refers to another collection, juste for you to know.

I already made a query which gets me all the points near a precise location :

db.point.createIndex({ 'localisations.location': "2dsphere" })  

db.point.find({  
    'localisations.location': {  
        $near: {  
            $geometry: { type: "Point",  coordinates: [ 48.8588377, 2.2770207 ] },  
            $minDistance: 0,  
            $maxDistance: 100000  
        }  
    } 
})  

Now I would like to query all the points which are near a precise location AND those with a specific location_type_id.

TRIES AND FAILS
I tried many queries in the MongoDB shell but none of them produced a satisfying result.

Query 1 I think it doesn't return anything because location: isn't an exact field.

db.point.createIndex({ location: "2dsphere" })  

db.point.find({  
    'localisations': {  
        location_type_id: 1,  
        location: {  
            $near: {  
                $geometry: { type: "Point", coordinates: [ 48.8588377, 2.2770207 ] },  
                $minDistance: 0,  
                $maxDistance: 100000  
            }  
        }  
    }   
})  

Query 2
The main problem here is it gets me a point document if in the localisations field there is an object with a correct location_type_id and an object with the correct location. It is not necessarily the same object, which I want it to be.
see: https://docs.mongodb.com/manual/tutorial/query-array-of-documents/#combination-of-elements-satisfies-the-criteria - second paragraph at the end.

db.point.createIndex({ 'localisations.location': "2dsphere" })

db.point.find({  
    'localisations.location_type_id': 1,  
    'localisations.location': {  
        $near: {  
            $geometry: { type: "Point", coordinates: [ 48.8588377, 2.2770207 ] },  
            $minDistance: 0,  
            $maxDistance: 100000  
        }  
    }   
}) 

Query 3
I wanted to try this method : https://docs.mongodb.com/manual/tutorial/query-arrays/#query-for-an-array-element-that-meets-multiple-criteria

db.point.createIndex({ location: "2dsphere" })  

db.point.find({ 
    localisations: {   
        $elemMatch: {  
            location_type_id: 1, 
            location: { 
                $near: {   
                    $geometry: { type: "Point", coordinates: [ 48.8588377, 2.2770207 ] },  
                $minDistance: 0,  
                $maxDistance: 100000  
                }  
            }  
        }  
    }   
})

Unfortunately, I get this error:

Error: error: {  
    "ok" : 0,  
    "errmsg" : "geoNear must be top-level expr",  
    "code" : 2,  
    "codeName" : "BadValue"  
}  

Now you know everything, I hope you can help me.