1: You are writing to the UART without first checking if it has finished if it was ready sending the previous byte.

2: You are reading from the UART without checking first if something has come in. In this particular case, that's less of a problem than the above mentioned point (you'll simply read the last received byte over and over and over...)

3: At 9600 baud, you will not have any significant audio frequency range. At 9600 baud, you will be able to transmit about 1000 bytes per second. The highest audio frequency you can transmit at that rate is half of that: 500 Hz. If you try to send higher frequencies, this will lead to what is called "aliasing", and much of what you are hearing is probably that.
To increase the audio bandwidth, increase the baud rate. For telephone quality you will need up to 3500 Hz, so about 70000 baud. Also, provide good filtering on the DA output, but more importantly in the AD input to filter out anything above the maximum frequency you can transmit at your given rate, or it will lead to aliasing again.
Finally, for good quality digital audio, timing is all important. Your sampling frequency at both in- and output should be exactly synchronized. If you leave your timing to whatever your program takes to execution each loop, do not expect too good results.

I STRONGLY suggest you first do some basic reading on digital audio and signal processing before you continue down this road. You may well find that much more is required than you suspect.