TestMongoose.hx

import js.npm.mongoose.Model;
import js.npm.mongoose.Schema;
import js.npm.Mongoose;

class TestMongoose {
  public static function main(){
    
    Mongoose._.connect( 'mongodb://localhost/test' , cast start );
    
  }
  static function start(err){
    
    if( err != null ){
      trace(err);
      return;
    }
    
    var schema = new Schema({
      title : String,
      content : String,
      date : Date
    });
    
    var model : Models<Dynamic> = Mongoose._.model('Article',schema);
    
    // créer un article
    model.create({ title : 'My New Article', content : 'Bla bla'}, function(err, article){
      if( err == null || article == null ){
        throw "Error saving article...";
      }
      
      // mise à jour de l'article
      article.date = Date.now();
      article.save();
    });
    
  } 
  
}

Ok sorry for the late reply
but I actually didn't get any notification or email whatsoever.
Anyway...

js.npm.Mongoose._ is just what is returned by require('mongoose')
Calling require('mongoose') in JS actually returns an instance of Mongoose (ie js.npm.mongoose.Mongoose in Haxe/JS), I guess because most setups will only use one Mongoose instance.
It's a kind of weird singleton pattern used by the library maintainters...

So you can indeed connect to your database using Mongoose._.connect, and then use Mongoose._.model, etc
I decided to 'translate' the pattern this way in Haxe...
I could have made these static methods of js.npm.Mongoose to simplify usability, but it would have required to duplicate signatures in js.npm.Mongoose (static) and js.npm.mongoose.Mongoose (instance methods).

I believe some day I'll just remove this possibility, to enforce users to instanciate Mongoose themselves like this (which is IMHO cleaner and feels less hacky from a Haxe POV) :

var db = new js.npm.mongoose.Mongoose();
db.connect('...');
var article = db.model( new Schema( { ... } ) );

As for this error you get, I don't really manage to reproduce...
Now the extern is not 100% complete / tested for sure, so you may indeed need to cast here and there.
Don't hesitate to file issues in case you believe it needs to be fixed.
PS:
I re-read the source from which I pulled this example,
and realize the model variable is actually typed js.npm.mongoose.Model.Models
This should do the trick.
I'll change the example accordingly

About save it indeed requires a callback,
At least, the extern does,
Not sure if mongoose actually requires it...

I've updated the example with code to connect to a local mongo instance.

Also, regarding Haxe typing (to address your error with Null<js.npm.mongoose.Model<js.npm.mongoose.Schema>> has no field date)
... I just commited a change so Document (and thus Model) implements Dynamic
This should remove the error, and makes sense until we find a proper way to type Documents / Schemas / Models ...