When hand-washing dishes I like a double sink. But then its not really used except to let the dishes drip dry in on a wire rack that I have laying across the second sink. Way back when I was single and had roommates we use one sink to hold dirty dishes and the other one free to use as a sink.
A lot of newer faucets have the integrated pull out sprayer. I find these better and more useful than the old awkward hose sprayers which rarely got used except to spay me in the face when I grab it wrong...
These integrated types take up less holes. Some models use only one hole total for spigot/sprayer and H&C water valves. So changing the faucet to one of these may give you extra holes for the air gap. At one house filled 2 unused holes with pump dispensers for liquid hand soap and dish washing liquid. Then she wanted a hand lotion dispenser...
The fixture I have now has pullout sprayer and covers 3 holes. 1 is soap dispenser (built into the fixture flange), 1 for everything else, 1 hole is not used but covered by the flange.
Having to have an air gap depends on how the dishwasher and drain is installed. I don't remember the details. Something to do with how high the drain hose is in relation to the connection point. Look at the dishwasher installation manual. The last dishwasher I installed did not need one as per the installation instructions. I believe I used the high loop method. As someone else said codes may require one regardless. I've seen some air gaps put into the counter top would not recommend that.
Kevin