As I mentioned in the comments, you should give some more clarity in your question to give a truly tailored answer.
But, from what you stated above, I can help you break down your seemingly 6 steps into 3:
1) Copy a layer/layers
2) Make a new Document
3) place/drag them into the new document
Step 1: Duplicate
Do you know about the Duplicate Layers from the context menu?
- Simply select the layer(s) you want to copy into a new document.
- Right-click and select Duplicate Layers.
- When the box pops up, select New in the document dropdown.
You can even give the new document a name from this menu.
4) Trim the image to size
Step 2: Trim
Use the Crop tool if needed. The above Duplicate Layer step will create a file with the same dimensions as the file it came from.
5) Save as a PNG File
6) Then reduce their sizes to half and re-save
Step 3: Save
This can be consolidated into 1 step by using the File > Save As Web & Devices (Ctrl + Alt + Shift + S) command.
Here you will get a preview of how it will look, and how it looks currently in Photoshop. This way you can see any compression effects. You can also alter settings of PNG to reduce the file size.
These steps should help you with your workflow, but depending on some more detail you provide, you could create a Batch Action as well.