I know that you can copy a conditional format and apply it to another cell or another sheet in the same exact document, but is there a way to take a format from one document and add it to another new document?
It depends.
You surely don’t copy formats, but -via a clipboard- contents and attributes of cells or ranges.
If you do an unrestricted Paste
(not Special...
) into a new document, and the copied range had a ConditionalFormat or specific attributes or assigned named styles, this all will be transferred.
Concerning the named styles:
They will be created if missing, but named styles already existing in the target document will not be overwritten with different attributes.
Concerning the CF:
If it has formulas, you should expect errors. References used for them may simply not work in the target sheet.
Anyway:
Simply try if whatever you want to achieve does work. Probably there isn’t an exhaustive reliable specification.