Renaming and moving
Select a file and press Return to rename it, or drag it into another folder on the phone. Case-only renames (photo.jpg to Photo.jpg) work too, even though Android's storage ignores letter case.
The phone's Trash
Move to Trash moves a file into a Trash folder on the phone, so you can still get it back. Empty Trash removes it for good. To delete without the Trash, choose Delete Permanently… from Finder's menu; PortLine asks you to confirm.
Moving files off the phone
Move Selected to Mac… copies the selection to a folder on your Mac and removes each file from the phone only once its copy is complete. It's the safe way to free space.
Questions
Is renaming safe if the cable comes out?
Yes. Each change is recorded before it's sent and checked afterwards; an interrupted change is finished or undone when the phone is back.