Looks like those areas are extremely shady. If so, you won't get much grass growth in any of those spots.

Thanks for your feedback. What are my options to cover those bare spots - stones, shrubs, etc?

I did rocks and plants in similar shady spots. Check out Hosta's which grow well in shade.

What is the height under the deck? If it is high enough would it be practice to make a covered patio under the deck.

Again if it is high enough you could enclose it and use it for yard tools, and other types of storage.

There are many extreme shade plants that you could use such as those mentioned. BUT, because of the shade this area is always going to be a problem.

Thanks for all the usefull feedback. The height of the deck is about 6 ft.

you might be able to get mint to grow in those shady spots, it looks like it gets dappled light. But be careful, it might take over your yard. If it was my place, I would put down pavers, edge with smooth pebbles, and try to get some mint to grow in between.