Your dead spots look like dead or dormant annual rye grass to me. In Iowa rye grass both annual and perennial grow very nicely in May thru July. But often it goes dormant or dies out in August. I've been over seeding my Iowa lawn each year with about 50% Tall Turf Fescue and 50% Kentucky Blue Grass The TTF is used in the sunny areas and the KBG in the shadier spots under my trees. Crab grass (aka) water grass in Iowa is easy to spot ... it looks like this. To kill it use Trimec or 2-4D on it. Halts will work to help prevent it's spreading but, you can not over seed when halts in on the ground. As it will prevent the good grass from germinating too.

There are alot of variables. Is the area where you want the pad level? Does it have to be cut out with a bobcat or something. Do you have a place for the dirt to go or will they have to get rid of it. Usually you can get a square foot price to finish over the phone. I cut out the ground, formed my own pad, installed the gravel and leveled it. Then I paid 75 cents a square foot to have it finished. You need roughly 13 yards of concrete(85 dollars a yard here) if your pad is 4" thick, plus a load of washed gravel as a base.($200) I know its broad but somewhere between 4 and 6k. Get a couple of bids, but worry more about the concrete guys reputation than his price. If the cheapest guy makes a mistake its permanent!

Someone above was wondering why chickens and not ducks on weather vanes. I really don't know, but I can put forth a guess. On US farms a century ago, most had chickens and roosters running loose (free range) but not many ducks. Ducks are water loving birds and will leave the barnyard if they find a pond or stream nearby. Chickens will range around the hen house, but always come back to the hen house to roost at night or for shelter during a storm. Its the Rooster that appears on weather vanes. His tail feathers are more ornate than the hen. Farmers observed the behavior of chickens as a weather forecaster. Chickens will head for shelter during a brief shower and wait for the rain to let up before venturing out again. An old saying was present in the community I once lived in. It was said that if the chickens came out in the rain, it will be a long rain lasting perhaps most of the day or more. By this, it would be natural to associate a weather cock with a wind vane. Wind vane? Its called a weather vane I do believe.

@Tim Cleary I have to admit, that part of the reasons why I'm reluctant to fill it, is that myself (or future buyer) can have the option to convert it into a underground studio like you said in the future, with part of the "deck" (or ceiling of the studio) being glass.... I have seen something similar in commercial property (like entryway to a subway), but not sure if such thing is realistic in residential...