They will shut down your instance, if you don't use it for an hour or two - and then it will take like 8-10 seconds to load it again. If you can live with that, I guess that would work, yes.

Heroku employee here, don't abuse the free. It's there for a design/prototyping/staging and as long as people don't abuse it will stay that way.

Depending on what you need to do to show off the product, absolutely. A static landing page should withstand just about anything you throw at it.