Accessing RS232 Rx Tx instead of OTG on stellaris LM4F232H5QD evaluation board
PA0 on your LM4F232 eval board is U0RX, that is, it receive data from others; PA1 is U0TX, that is, it transmit data to others. So you should connect your converters Rx to PA1, and Tx to PA0. It seems you mistake them.
Note: It seems the PA0 and PA1 have connections to the on board ICDI, check if there are jumpers to break the connections before connecting your converter.
Ax, Ay, and Az is the buffered Accelerometer BM140's Ax, Ay, Az analogue output. You can connect them to the ADC input of the MCU (already on your eval board, so you don't need buy new ones). Their may have jumps to configure this. 


All the needed information can be fund in the user manual of the eval board.