Iceland is arguably the best place in the world to see Gyr Falcon but it's generally not easy to see or to get close photographs. August is actually a good time to see it as the young are out and about and if you go to north-east Iceland in August you probably will see it and you might get good close views of it but not guaranteed at all. I saw 4 birds when I was in NE Iceland last August (not birding, just travelling with my kids).
Harlequin is generally easy to see in Iceland, except in August and September. In August the males have left their breeding grounds and are moulting in eclipse plumage at sea (where you can still see them). Females and young will still be on the rivers but if you want good photographic opportunities of male Harlequins then August is not a good time.
Arctic Fox is widespread but generally shy except for the Hornstrandir reserve in northwest Iceland, where they are tame and approachable. However, visiting this area takes a bit of planning and requires a boat trip and camping. There are no roads.
Do you mean seabird colonies? Again. August is a bit late for most seabird colonies and most species will have left in August, although there will still be Fulmars, Kittiwakes and Puffins in most colonies but Razorbill and Common and Brunnich's Guillemot will be absent in August.
No it is not a cold desert in August and there are plenty of birds around but not as much as in May/June when breeding birds are everywhere. Some inland areas will already be starting to get quiet and quite a lot of migrants will already have left.
Iceland is expensive, depending on exchange rates it is often the most expensive country in the world.
