I would stain the flooring, paint can peel and be a bother. For me, I'd stain it dark but that's a personal call. Painting a bright green when the rest of the colors are muted may be too much pop. How about a light green that is in the historical colors so it's muted a bit. I love apple green but muted a tiny bit.

All the same color because it's essentially one in the same element. In other words, you can have a door with no side lights but you can't have side lights without a door. That's why it doesn't make sense to paint the side lights a different color from the door.

Should the color of your front door or doors be the same color inside?

I love the door! Right now it looks pretty good white. Can you show us a pic farther back? (Like the first pic you posted?) I can't tell you the color name I used in my mockup because I did it in photoshop. I suggest dusty turquoise or sage, which will compliment red/orange. Don't go too saturated, it would be too bold next to those bricks. Maybe Drizzle, Vintage Vessel or Composed (below)? You're in a rush, but don't rush too much. You will still want to paint big samples. You may love a color in the store or online and find that you hate it in the actual surroundings.