You should not leave any marks on the part that gets printed because, well, then it'd show up on your printed cards!
Find out how much bleed the printer requires for your job. Set this as usual in your InDesign document; then add an extra slug amount. The Bleed is for printed content that may (usually accidentally!) appear on the extreme borders of your card. The Slug is 'throw-away' space, intended to put in everything you want the printer to know but should not appear on the final content.
For a fold-job, you can put dashed lines in the slug at the top and bottom (and not continuing over the main 'body' of the design). You can also add some text next to it, e.g., "fold inward" and "fold outward".
As an alternative, send two PDFs to your printer: one with the plain design, the other with all fold lines clearly marked and explained, along with a large "NOT FOR PRODUCTION" straight through the design - just to make that clear.