It's been a long tie since I played the game, but I here's my answers to your questions:
Ixamyakxim: Any pointers? Should I focus on the main story and learn the game as I play? Is there anything about the game I should know right off that I might miss? Do I just suck it up, play and see what happens?
Well there's a lot of side stuff to do in this game. One thing you should know is that the true ending is only accessed if you complete everything in the game, including the Riddler trophies.
If you like the game and don't get bore easily, I'd say go for it. Do some main story missions to move the game forward, then do some side stuff, and so on. Try to balance, so you don't get fed up of one or another.
Ixamyakxim: But yeah, really cool game I'm just worried I might miss certain stuff because I'm drowning in the interface. Even the combos make my head spin - or will it all start to come naturally after I get used to it?
For me it was natural, since I played the previous games. Like any other game, it might take some time to get used to it. I think the more you play, the more comfortable you will feel.
Ixamyakxim: Also, I get little "blurbs" saying there's a riot, or hear criminals talk about "things" - should I be responding to these? How do I find their source? Detective mode? What should I be looking for?
Yeah, I think detective mode is what you need to use. However, If I remember correctly, these riots are not important, nor considered side stuff necessary for the true ending, so you can ignore it (not truly sure, though).
Ixamyakxim: Oh and the tightrope - super cool idea - but do I need it selected as my gadget before I can use it in flight? Or can I just hold the button (I think one of the thumbsticks?) and it fires off?
You mean the grappling gun that enables you to move through the city? If it's that, then no. While gliding you just need to look to the building you want to grapple to, then the reticle appears and you just have to press the corresponding button to grapple.