I think it is always a good idea to go to your town planning office and speak to someone about what would be required in terms of zoning and permits, and the schedules for obtaining those. Obviously it depends on the town, but our staff is very helpful in this regards. If your house is a typical one for the area they may also know of similar work other people have done which might give you ideas. And for us it was nice that when they saw who our architect was they were familiar with him - we needed a variance and that smoothed the process. Same thing for the contractor - our inspections have occurred without delay (fingers crossed).

It will likely be cheaper and faster to remove the center section and start over. So that said let your architect draw whatever works best on the rear ignoring what is there now.

Half that addition chunk is attached to the back of the house. What does the back of the house look like? From what I can tell from the photos, there is a second story balcony that might be eliminated? Instead of a single story entrance bit attached to the box on the back of the house. Perhaps consider doing that corner a full two story with the roofline creating a corner/L turn. Might depend a bit on what the back of the house looks like and what the addition connection there looks/behaves like. It might also depend a bit on if your municipality has codes and regulations on this. As in how much square footage an addition can be, that sort of thing.

Appropriate watering for new sod is 3x daily for 5 to 20 minutes each time continuing for 2-3 weeks before backing off on the watering frequency. Never let the soil get soggy/mushy. The idea is to keep the soil that came with the sod moist as well as the underlying soil/sand. If you have a coarse sandy soil, then you should water more than 3x per day. You also might try covering the grass with burlap or other shade cloth. Is it a big area? If you can save any of it, then it will eventually spread to fill the rest.