You're nearly there...
Assuming you're right regarding the requirements of your Zigbee interface (I don't KNOW that is what it requires, but believe it is) then 'Yes' to (1) - you can use the commands you've identified to communicate with a UART peripheral connected to a Nios processor.
However, I think you're code isn't quite what you want.
You've correctly identified that you need to test the UART's 'STATUS' register. I assume you're intending to test whether there is a new receive character in the receive buffer. However, for that your bit mask and AND operator are incorrect.
When a new character is available in the 'RXDATA' register, the 'rrdy' bit is set in the 'STATUS' register. That is bit 7 of the 'STATUS'.
So you need to test
if(IORD_ALTERA_AVALON_UART_STATUS(UART1_BASE) & 0X80)
to establish whether there is a valid character in the receive buffer.
Your current test is testing the status of 3 bits of the 'STATUS' register - transmit empty, transmit ready & receive char ready. I'm not sure why you would want to test those three bits at the same time.