Your turf looks good, wish all my customers gave a shit like you do, my job would be a lot easier.
1. Yes, deep and infrequent watering is the way to go, water the piss out of it and the deeper the water goes in the soil column the deeper the roots go to get the water. Deep rooted bermuda grass is healthy and very drought tolerant. Water around once a week about 1 to 1.5 inches and when its hotter than hell twice a week is all it needs.
2. Not sold on the soil tests. You can send in 10 different samples from your yard and I guarantee you will get 6 to 8 different recommendations on what your soil needs. New sod needs a good starter fert like a 18-24-12, you need your middle number, phosphorous high and you'll be good. After that like you know it needs a fuck load of nitrogen. Almost every accurate soil sample will show all bermuda needs is nitrogen.
3. Fert schedule, first of May (depending on your location) 46-0-0 100% slow release, it will last 8 weeks. end of June first of July another 46-0-0. Mid August use a winterizer, something like a 5-0-30 this is important, you dont want to put down a high rate of Nitrogen late in the year, it can cause a shit load of disease including spring dead spot, you dont was that shit.
4. Yes, bermuda mows and looks better if the soil is level, if it were me I wouldn't use a compost/sand mix. I would use a rich mix topsoil. Rich mix has a lot less weeds than compost and sand. Vey few fungal issues with bermuda other than to much water when its cool but nothing that needs to be treated.
5. If I knew your city I could help you with a pre emergent schedule. Late February is to late for the first pre m of the year.
3.