Can I use Blender Python to customize a new node type? Can the function achieved by the node be defined itself? 
Do you mean a new Nodetree type, or a node for an existing Nodetree type?
In case of a builtin Nodetree type, you might need to add the functionality to the source code (unless you just use functions already available in those Nodetrees). For your own custom Nodetrees, you need to implement all functionality by yourself.
new Nodetree type, I add properties to existing nodes will destroy its own node function, and the added properties can only be existing properties of Blender.
For new Nodetree types, you need to write your own nodes and how they (and their nodetree) should work. You can’t reuse nodes from other systems.
Can I create new Nodetree types with Blender Python? For help 
Yes you can. Check the python templates that come with Blender. There’s one for Custom Nodes.
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I ran python templates, but no new nodes were found. Can you tell me where I can find the newly defined nodes? Thank you for your help 
If you executed the ‘Custom Nodes’ template, there should be a new editor called ‘Custom Node Tree’. In there, if you create a new nodetree, you’ll have three nodeitems in your add menu (they represent the same node, one with its default values, and two with custom values).
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