Q1: Can I increase the output volume at least 6db up without additional amp?

A1: The module has a 1W amp and you don't need to use any additional amp for 6db only. I guess you connected the wrong pin outs from the module. You need to connect the pin 13 and pin 14 of the module to the 1W 8Ohm speaker. Which pins were you using?, pin 8 and pin 9? Through these two pins the module actually need to work with an external amplifier/active speaker. 

Q2: Can the module automatically keep max output volume or it will go to default level after every disconnecting/connecting the power voltage?

A2: It automatically keeps the max output volume. 

Q3: How can you ad volume control using the ADKEY. 

Q3: See page 18 through 20 of datasheet for the updated ADKEY control connection. For button with 20K resistor, a short key press will change the track while a longer key press will reduce volume.

Q4: Can I set the audio recording quality(bit rate) using the ADKEY? 

A4: In ADKEY mode, the default audio recording quality (bit rate) is 128Kbps, which can't be changed. 

Q5: How do you record stereo sound using the ADKEY? 

A5: In ADKEY mode, it is only possible to record mono sound.  To record stereo sound it is necessary to send serial commands using MCU or Arduino and use the AUX input mode.