Does it happen only with notes, or everytime you make any kind of domestic changes, the total amount is changed?

For multi-shipment it is happening for every domestic change.

Another thing i noticed when i am doing multishipment after payment the status in  [dbo].[OrderFormPayment] 

is Pending.

I think it should be Processed.

Can you explain how this could be happen.

I noticed also after adding note the Shipping cost is being disappeared .

I can't reproduce the problem on Quicksilver. I suppose it relates to your implementation/configuration. WOuld suggest you to contact out support service for assistance.

Whenever you press "Save" after edits have been made on a PurchaseOrder, Commerce Manager runs the workflow named "SaveChangesWorkflow". This could point to different classes depending on whether you have activated the VNext workflows or not. It can be "POSaveChangesActivityFlow.cs" or "POSaveChangesVNextActivityFlow.cs".

Either way they run Activities that:

1. Adjusts inventory (something might happen here in your case)
2. Process payments
3. Calculate order totals

This happens no matter what has been changed on the PurchaseOrder, be it adding an OrderNote or changing the line items.

So in your case there is probably something happening in step 1 above which in turn causes the numbers to change when step 3 happens.

The code that is triggered when you press the "Save" button can be found here (requires some kind of decompiling software to inspect in detail though): 
Mediachase.Commerce.Manager.Order.CommandHandlers.PurchaseOrderHandlers.SaveChangesHandler
But unless you have an understanding of webforms and Commerce Manager in general, I do not recommend changing things here.

What you could do is look at what running this workflow does to your PurchaseOrder. What is built in might not be entirely compatible with your setup or could do things that you don't want it to in your specific case. If you don't have the source code for the workflows project, you can find it here under the Episerver Commerce Section:
http://world.episerver.com/download2/

Hope this was helpful in your further investigations.