I'm going to say something that's more than likely going to be taken out of context for people to jump down my throat for, but hear me out: people don't use maps for navigation.
On any scale beyond your basic shopping center map, they aren't going to be nearly as useful as landmarks. Ok, yes, you need a map to get a vague idea of what's near where, but that doesn't need to be particularly accurate. Does it really affect your driving if the roads on an atlas are a few degrees off, or centimeters too long, or do you just care about the road names and junctions?
Even at sea, they use the stars as reference points. All they really need a map for is to work out which constellation to head for, and by the time they get closer they can just use their eyes. Ok, we can see land, it has that feature which exists there, so we want to head that way... You don't need a particularly accurate map for any of that.
Landmarks are the most important part of navigation, far more than a 100% accurate map. A sketched out sheet that notes down roughly how they relate to each other is as useful as the most accurate flat or spherical map in the world, and even that can be replaced by a few notes. If you try to follow a map alone by, say, ship, you're going to get screwed over in your first day at sea if your angle isn't accurate to within 0.01 degrees, or if there's a single wave or odd wind that adjusts that angle. That's true for any journey, there's no perfect means to point yourself in one direction and go, so the means to course correct are required for navigation, and that's where landmarks come in. 'Head 100km 10 degrees from North,' isn't nearly as useful as 'take the third left, if you reach Burger King you've gone too far.'
So in answer to your question:
1. Yes, there are flat Earth maps that work just fine so long as you use your common sense.
2. No, they don't work alone, but then no map does.