Thanks a lot for taking the time to go through the device's datasheet and explain the solution so patiently.
Bless you ! Thanks !

according to PFC8591 datasheet, the A/D converter can transmit more channels in one response - using auto-increment flag. It means that if you send control byte 0x04 and read 3 bytes, you will get previously converted byte (and probably throw it away) and 2 bytes (channel 0 and channel 1).

PFC8591 is 8bit ADC - it means that you don't have to combine two received bytes into one analog input:

//analog_in1 = (i2c_bufRx[0]<<8) + i2c_bufRx[1];
analog_in1 = i2c_bufRx[1];

I changed your code, mainly Configuration register table for your information and control byte command. See the code:

//assigning variables to outputs, these variables are WRITE-ONLY
//long output(0) adc_value;

long output(0) analog_in1;
long output(1) analog_in2;


//declaration of variables
long i2c_bufTx[3]; //buffer for transmitting data
long i2c_bufRx[3]; //buffer for receiving data
long i2c_bus_handle;
long i2c_chip_address;
long i2c_write_count;
long i2c_read_count;
long i2c_ret_fun;


//long output(2) freq;


//the init procedure is executed once when the REXLANG function block initializes
int init(void)
{
  i2c_bus_handle = Open(I2CDEV_FNAME); // open I2C bus
  /* Address: 1 1 0 1 A2 A1 A0 */
  i2c_chip_address = 0x48; // 7-bit address of the I2C device
  
  
  return 0;
}

//the main procedure is executed once in each sampling period
long main(void)
{
  /* Configuration register: 
     ===============================================================================================================
     | bit 7 | bit 6                    | bit 5-4                    | bit 3 |  bit 2             | bit 1-0        |
     ---------------------------------------------------------------------------------------------------------------
     | 0     | 1 = Analog output enable | 00 = single ended inputs   | 0     | 1 = auto-increment | 00 = channel 0 |
     |       |                          | 01 = 3 differential inputs |       |                    | 01 = channel 1 |
     |       |                          | 10 = mixed inputs          |       |                    | 10 = channel 2 |
     |       |                          | 11 = 2 differential inputs |       |                    | 11 = channel 3 |
     ===============================================================================================================
  */
  i2c_bufTx[0] = 0x04; // read channel 0 with auto-increment flag (00000100b)
  i2c_write_count = 1;
  i2c_read_count = 3;
  //Sending data via I2C
  i2c_ret_fun = I2C(i2c_bus_handle, i2c_chip_address, i2c_bufTx, i2c_write_count, i2c_bufRx, i2c_read_count);
  //some old data in i2c_bufRx[0] from previous conversion
  analog_in1 = i2c_bufRx[1];
  analog_in2 = i2c_bufRx[2];
  
 

  return 0;
}

//the exit procedure is executed once when the task is correctly terminated
// (system shutdown, downloading new control algorithm, etc.)
long exit(void)
{
  if(i2c_bus_handle>=0) Close(i2c_bus_handle); // close I2C bus
  return 0;

Unfortunately we don't have this AD converter in stock so we couldn't test it.
Hope it will help you.

I am unable to figure out what buffers to define to read multiple analog input channels of the PCF8591 A/D converter. I am able to read only the first channel successfully. The device address and the input channel addresses are correct. Please have a look at my code.

//assigning variables to outputs, these variables are WRITE-ONLY
//long output(0) adc_value;

long output(0) analog_in1;
long output(1) analog_in2;

//declaration of variables
long i2c_bufTx[3]; //buffer for transmitting data
long i2c_bufRx[3]; //buffer for receiving data
long i2c_bus_handle;
long i2c_chip_address;
long i2c_write_count;
long i2c_read_count;
long i2c_ret_fun;

//long output(2) freq;

//the init procedure is executed once when the REXLANG function block initializes
int init(void)
{
  i2c_bus_handle = Open(I2CDEV_FNAME); // open I2C bus
  /* Address: 1 1 0 1 A2 A1 A0 */
  i2c_chip_address = 0x48; // 7-bit address of the I2C device
 
 
  return 0;
}

//the main procedure is executed once in each sampling period
long main(void)
{
  /* Configuration register:
     =====================================================================================
     | bit 7              | bit 6-5        | bit 4          | bit 3-2     | bit 1-0      |
     -------------------------------------------------------------------------------------
     | 1=start conversion | 00 = channel 1 | 1 = continuous | 00 = 12-bit | 00 = gain x1 |
     | 0=no effect        | 01 = channel 2 | 0 = one-shot   | 01 = 14-bit | 01 = gain x2 |
     |                    |                |                | 10 = 16-bit | 10 = gain x4 |
     |                    |                |                | 11 = 18-bit | 11 = gain 8x |
     =====================================================================================
  */
  i2c_bufTx[0] = 0x00; // read channel 1 .I am able to read channel 1 successfully
  i2c_bufTx[0] = 0x01; // read channel 2 
  i2c_write_count = 1;
  i2c_read_count = 2;
  //Sending data via I2C
  i2c_ret_fun = I2C(i2c_bus_handle, i2c_chip_address, i2c_bufTx, i2c_write_count, i2c_bufRx, i2c_read_count);
  analog_in1 = (i2c_bufRx[0]<<8) + i2c_bufRx[1];
  analog_in2 = (i2c_bufRx[0]<<8) + i2c_bufRx[1];
 
 

  return 0;
}

//the exit procedure is executed once when the task is correctly terminated
// (system shutdown, downloading new control algorithm, etc.)
long exit(void)
{
  if(i2c_bus_handle>=0) Close(i2c_bus_handle); // close I2C bus
  return 0;