Can I apply a watermark/logo in the form of a png or by using the brush tool when batch process files in photoshop elements 9?
If you use a watermark brush, it is necessary to appy it manually to each file.
However, you can batch process from Editor via File menu>Process multiple files. Look in the drop-down under labels in the dialog.
There are multiple ways to add captions/watermark/copyright info in Photoshop Elements
Below KB articales should be helpful in this context depending on your need and usage and expertise