If you put the dishwasher next to or near the sink, you can probably tie into the sink's hot water supply (as well as the sink's drain). If you are new to plumbing, there are "compression fittings" that are simple to use but more expensive in the long run than using pex only fittings & crimpers or cpvc fittings or copper & flux fittings. "Near" meaning a cabinet away or so - in which case supply & drain lines will likely run through the lower back of that cabinet. Our dishwasher has a 12" cabinet between it & the sink, works fine.
For drainage, using an air gap may be a regional thing. From what I've seen, West coast uses air gaps, northeast doesn't. If your code requires it, put one in. Otherwise, as long as the kitchen sink drain is properly vented you shouldn't really need an air gap.