Mimi....I'm not understanding your question could you repeat please?
Not sure what to do about narrow flowerbed. Need something I do not have to water
It depends on where you live. I would use the same groundcover plant and let it go. Succulents work, especially with the heat retained by the bricks and cement. Otherwise, that is a spot where I would use Bishop's weed, also called Snow on the Mountain. It would be contained there. Bishop's weed is a VERY invasive plant,but it is great for a tough spot.