I'd go with the Corsican mint......creeping thymes would really prefer to be in full sun and a northern siting with minimal winter sunlight is not going to be their cup of tea :-) Ask at your local nursery/garden center for the availability of growers flats. These are solid (no pots) flats of groundcovers that are typically used by landscapers, although helpful for homeowners with large areas to cover. They tend to be about 1/2 the cost of potted plants. With low, mat-like, root-as-they-go groundcovers, you can just separate appropriately sized plugs and plant in between the pavers. Each plug will have enough roots for the plants to 'take'. And you can space the plugs to fill in according to the spacing of the flags and your needs, not by some prescribed spacing that may not apply to your situation. Groundcover seeds are not easy to find but that would be an equally inexpensive approach although much slower.

You can caulk and paint to match wall color. We did that with our last house (circa 1834) because, even after we remodeled, walls were not straight.

Since you want the rise on the steps to be consistent, raising the sidewalk appears to be the best approach.

As others said: caulk. If you tried wood filler, you would end up with having to sand here and there and it becomes a mess. And cracks would open in the future. Use latex caulk and immediately smooth the caulk line with a moist-to-damp paper towel. This will make it very neat, and remove any residual caulk that has spilled over onto the wood surfaces. Once you tape and paint it will look just fine.