New Rx-8 Owner Some issues?

Okay so where do I start. For awhile I've been eyeing the Rx-8 . . . a couple weeks ago I bought one. I knew they were delicate and required extra care and love as well as money. So far I haven't put any money into it, which pretty much means it is very well taken care of for the 144, thousand miles on it. A lot of miles on it I know. The previous owner had just changed out all of the coils, wires, new battery, new brakes, and several other things. I knew from looking at it that it was going to need new tires. So currently saving up for that. To make this short 05 Rx-8, Tire pressure light flashes 20-30 minutes in to the ride. Several have told me that not only will I need new tires, they need a good alignment done. With that said POWER STEERING. Another light that turns on. For the most part I've noticed it come on if I ever drive over 50, or that can translate into when the car is "hot" . . . or pretty much any rough driving. My thesis is tires are giving the power steering a false alarm, while others tell me it could be the actual power steering. I might not be having a good start with my 8 but I don't want to give up on it! What would the next steps be? And if you have any other tips or advice that would help too, besides that I will be reading this forum like there is no tomorrow . . .

located in Phoenix, AZ.