How do you update objects in a document's array (nested updating)

For question #1, let's break it into two parts. First, increment any document that has "items.item_name" equal to "my_item_two". For this you'll have to use the positional "$" operator. Something like:

 db.bar.update( {user_id : 123456 , "items.item_name" : "my_item_two" } , 
                {$inc : {"items.$.price" : 1} } , 
                false , 
                true);

Note that this will only increment the first matched subdocument in any array (so if you have another document in the array with "item_name" equal to "my_item_two", it won't get incremented). But this might be what you want.

The second part is trickier. We can push a new item to an array without a "my_item_two" as follows:

 db.bar.update( {user_id : 123456, "items.item_name" : {$ne : "my_item_two" }} , 
                {$addToSet : {"items" : {'item_name' : "my_item_two" , 'price' : 1 }} } ,
                false , 
                true);

For your question #2, the answer is easier. To increment the total and the price of item_three in any document that contains "my_item_three," you can use the $inc operator on multiple fields at the same time. Something like:

db.bar.update( {"items.item_name" : {$ne : "my_item_three" }} ,
               {$inc : {total : 1 , "items.$.price" : 1}} ,
               false ,
               true);

There is no way to do this in single query. You have to search the document in first query:

If document exists:

db.bar.update( {user_id : 123456 , "items.item_name" : "my_item_two" } , 
                {$inc : {"items.$.price" : 1} } , 
                false , 
                true);

Else

db.bar.update( {user_id : 123456 } , 
                {$addToSet : {"items" : {'item_name' : "my_item_two" , 'price' : 1 }} } ,
                false , 
                true);

No need to add condition {$ne : "my_item_two" }.

Also in multithreaded enviourment you have to be careful that only one thread can execute the second (insert case, if document did not found) at a time, otherwise duplicate embed documents will be inserted.

We can use $set operator to update the nested array inside object filed update the value

db.getCollection('geolocations').update( 
   {
       "_id" : ObjectId("5bd3013ac714ea4959f80115"), 
       "geolocation.country" : "United States of America"
   }, 
   { $set: 
       {
           "geolocation.$.country" : "USA"
       } 
    }, 
   false,
   true
);

One way to ensure there are no duplicates of the "item_name" fields would be the do the same actions as given in the answer https://stackoverflow.com/a/10523963 for Question #1 but in reverse order!

Push into the document if "items.item_name":{"$ne":"my_name"} - the update filter MUST contain some uniquely indexed field! And upsert is false. Increment the document if "items.item_name":"my_name".

The first update should be atomic, thus it doesn't do anything if the array already contains the element with the item_name "my_name".

By the time the second update happens, there must be an array element with the "item_name"="my_name"