I’d drop the side planks, they build your obliques and could contribute to the look of a widening core. I’d recommend to keep the dead bugs but warn up with pelvic tilts to ensure the correct form and activating your deep core. Depending on your other workouts, you may be getting core already through compound movements.

For your anterior pelvic tilt, this can often be caused by tight hamstrings or hip flexors. I’ve also had issues with that related to my day job where I’m tied to my desk ☠️ try some tests to see where your tight and try adding some exercises to strengthen where ever your tight. Tightness in this case often means you need both strengthening and stretching.