The Duplicate and Delete options are specific to the file manager software, which in the case of ZorinOS Core, that is something called Nautilus. You can install another file manager if you prefer; a popular alternative is Nemo, created by Linux Mint for the Cinnamon desktop environment. Nemo does have the Delete option, but I'm not sure about Duplicate.
Another option is to add these options to Nautilus yourself:
As for the battery, I don't know. But check within Settings -> Power -> Power Mode. If "Power Save" is selected it may explain that behavior.