We can add a "bitmap" or image signature to a PDF file, either by using Adobe Acrobat or by Mac's Preview app, but I wonder, besides always encrypting it with a password before sending it by email to the other party, how valid and secure is it?

The reason is, if the signature is a bitmap, then there is nothing that prevents anybody copying and pasting that image to other documents, or even, if a cheque is written to anybody at all (such as to the landlord), then there is nothing that prevents the signature from being scanned and copied and pasted to any other PDF documents as well.