I have serious trouble finding anything useful in Mongo documentation about dealing with embedded documents. Let's say I have a following schema:

{
  _id: ObjectId,
  ...
  data: [
    {
      _childId: ObjectId // let's use custom name so we can distinguish them
      ...
    }
  ] 
}

1. What's the most efficient way to remove everything inside data for particular _id?

2. What's the most efficient way to remove embedded document with particular _childId inside given _id? What's the performance here, can _childId be indexed in order to achieve logarithmic (or similar) complexity instead of linear lookup? If so, how?

3. What's the most efficient way to insert a lot of (let's say a 1000) documents into data for given _id? And like above, can we get O(n log n) or similar complexity with proper indexing?

4. What's the most efficient way to get the count of documents inside data for given _id?