First issue throw out bearing. Second could be broken cat inside exhaust. This was the case with mine

 

The first issue sounds as though it is in fact throwout bearing related. When I bought my first 8 new, the throwout bearing was noisy and I was assured that the noise was normal. I hear the same sound on my BB 04 that I just installed a new Exedy clutch in. Sounded the same before the new engine and clutch as well and the old throwout bearing had zero play upon removal. Depending on the severity of the sound, it could in fact be a characteristic sound of the RX-8's throwout bearing.

The second issue could be a couple things. The first thing that comes to mind is rotor bearing failure. I experienced this on an 05 GT and the sound you are describing is exactly what I heard before I installed a new engine in the car. As stated above, inspect the catalytic converter for possible breakdown and inspect all under body heat shields and ensure they are tight and rattle free.