I had an FUE hair transplant 15 days ago. I have quite fair hair. Will my donor area thicken up? (Photo)

The short answer is yes.  All scars contract, and does take some time to do so.  The circular scars created by the FUE procedure will lighten, and contract on themselves over time. They will be about 85% healed at 6 months, and fully healed within 12 months.  In the meantime, your hair around the harvested area will grow longer.  It appears as though you had a linear procedure at the same time, as I see sutures in the donor area.  As long as you grow your hair out long enough to cover the linear scar from the linear procedure, the FUE scars should not be seen.  In terms of keratin fibers, it'd be best to wait a few days until after your sutures are out; roughly 5 days after the sutures are out.  You want the skin to be 100% healed over prior to using keratin fibers.

It all depends on how many grafts you had transplanted and how well the grafts will grow.  I am sure you can find answers here to assuage your anxiety but only time will tell.  You can apply any concealers at this stage or consider SMP when your donor area heals.

15 days is still pretty early. Your scarring will still fade over time (you and your doctor may want to discuss the use of Acell or something similar to promote healing), and your hair will grow out further, so I think it will be covered at some point. When all is said and done if you have to wear your hair longer than you'd like in order to cover the scar properly, you can get SMP to address the issue!
As for fibers, usually for FUE most people would say two weeks is enough of a wait time. But because of that linear scar, you should wait until that's out. Ask your doctor just to ensure there's not anything else that would be preventing you from using the fibers.

When you harvest from the donor area using  FUE technique you take hair out from the whole donor area. Some doctors go beyond the donor areas for larger sessions which will ultimately cause problems later on. However, the whole donor will look thinner as a result if donor hair depletion, and your donor hair in general may think thinner than other parts of the scalp. This is one of risks involved with doing large session FUE and should be discussed with a client before deciding on a harvesting technique.