Answer: When the flowers of your zinnias are spent, cut the flowering stems down to foliage level. As long as the weather is warm, they should send up new flowers.
You can dig and divide or transplant perennials now. The weather should be just fine from now until late September.
Grasses usually won't grow in shady areas which is probably why you haven't had success in the past. Grass needs all day sunshine in order to thrive. I wonder if the city would object to your planting an evergreen groundcover in the parking strip? There are a number of low growing groundcovers that will grow in the shade, but they will need to be watered regularly during the growing season.
Best wishes with your garden!
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