Congratulations on getting your first batch bottled! Very exciting!
Drip-drying your bottles is fine. I haven't used StarSan (usually use iodophor), but it's advertised as a no-rinse sanitizer. That's not a problem. You did fine.
Although it sounds kind of gross, the hair is probably not a problem. If it were a hair ball that would be a bigger deal... but just a hair is probably not that big a deal. I suppose it depends what kind of hair product she uses
Not adding the priming sugar right at the start is not a big deal either. I always add priming sugar
after I transfer all the beer into the bottling bucket. And just an FYI for next time: I never cool it. It'll kill a few yeast cells to add boiling syrup, but it won't kill even close to enough to be a problem. If you're making a pint of priming solution and you put that in five gallons of beer, you're putting in something like a fortieth of the volume. It'll cool faster in the beer, and it won't kill enough yeast to make a difference.
The biggest problem I see is the hot spots. If you left it for an hour after adding the sugar, it might exacerbate the problem. I.e. you've given it more time for the sugar to settle to the bottom.
But don't assume there's a problem: I made and bottled several batches without "gently stirring". True, I've had some dramatic volcanoes, but some of them worked just fine. And I've never actually exploded a bottle.
And look on the bright side: if you end up with some beer volcanoes, you'll remember for sure next time. "That'll learn you!"
One piece of advice you're free to disregard: when I'm unsure how even things are, or maybe the last few bottles look really yeasty, I put those aside as my sample bottles. Let's be honest: you're not going to wait the "proper" three or four weeks to sample your first batch: you're going to be wanting to open one tomorrow. So use your "iffy" bottles as your samples. If you don't know which ones are iffy, that's not a lot of help. But I've taken to deliberately segregating those as I bottle.
A related note: I read somewhere you learn a lot about beer by opening a bottle a week as it conditions. Whether or not you want to do that this time, I'd recommend it. I opened one a week on one batch and recorded tasting notes. It's amazing what happens to the flavours in the bottle.
On to more important matters: did you take an hydrometer sample? how did it taste?