As a user until I haven't interacted with the application/form before, I have no way of knowing that the auto-save will occur. I will only notice it if I read the documentation or, I accidentally close the app and find the form data present when I log in.
Also, from a developer's point of view it will be difficult to find the "right" time for auto-save. I am not sure when do you want the auto-save to work.
Scenario 1 : In a multi-stage form, when user goes from page x to page x+1
Scenario 2 : After every t minutes
Problems with Scenario 1 : User filled everything on page x+1 and the application crashes (or, machine accidentally shuts-down). He/She will have to fill the page x+1 again.
Problems with Scenario 2 : User filled everything on page x+1 and the application crashes (or, machine accidentally shuts-down) in 5.9 min. The stuff that he/she has written in those 2.9 minutes will be lost. (assuming t=3min)
Solution: Give the option to save the work. I always try to save the form when I have filled something important or long enough and I do not want to type all that again. Suppose, u r a customer support and you have got some long and important feedback from the customer and the app crashes. It will be difficult to get that feedback again. Visual "save" option will be handy in that scenario.
As far as the icon goes, floppy disc is the generic save option in most apps. I will suggest going with that as it is intuitive for the new user. I also suggest going for a layer (that will contain the visual "save" option) on top-of-the-form layer. The visual save option layer will stay on the right of the form field which is active. (Basically a floating layer)