Yes, that’s correct.
Yes, you spotted it. Good.
Is your study of modes an academic exercise mainly at the moment? I can recommend this topic: Modes Parts 1 - 9
If engaged in a modal discussion, it can be helpful to see all seven grouped together. One way of doing so often involves arranging together with Lydian at the top and Locrian at the bottom.
- Lydian → 1, 2, 3, #4, 5, 6, 7
- Ionian (Major) → 1, 2, 3, 4, 5, 6, 7
- Mixolydian → 1, 2, 3, 4, 5, 6, b7
- Dorian → 1, 2, b3, 4, 5, 6, b7
- Aeolian → 1, 2, b3, 4, 5, b6, b7
- Phrygian → 1, b2, b3, 4, 5, b6, b7
- Locrian → 1, b2, b3, 4, b5, b6, b7
The Major scale (the source of all these modes) - also called Ionian - is shown with all scale degrees emboldened. One scale above it is Lydian. Its one difference compared to major scale is the #4. This is shown in normal font. As you take successive steps down from the major scale, each new scale has one additional variation from the major scale. These changes are shown by removing the emboldened font at every step. Some describe going up from major as moving to something even brighter - the Lydian scale, and each step down as becoming darker.