From what you've described it sounds like the IAC has failed or is failing, that would make the RPM'S higher than normal. Just make sure you don't have any vacuum leaks, that's a good starting point.

TP sensors can cause all sort's of havoc. Their main characteristic is usually a hesitation like 383man said.
The best way I've found to check a TPS is via a DC voltage / waveform test.
Although, you have to have access to something like a Snap-on Vantage meter or a lab scope that shows waveforms.
But as long as you have a good multimeter, you can find out what each sensor is doing by reading the ohm's.
Here's a video I found that might help in your diagnosis....

http://www.wonderhowto.com/how-to/video/...l-motor-267188/