LED Driver Pin function
My question 1 - So, in that case, I want to understand whether this is
a synchronous boot LED Driver circuit ?

If you mean &quot;boost&quot; and not &quot;boot&quot; then no, it's not a synchronous boost circuit because it uses a standard diode here: -


I am asking because what should I connect to the GATE and GDRV pins
to?

You connect GDRV as per the above circuit. The gate pin needn't be used if you don't need the optional circuit shown above.

My question 2 - What would be the voltage at the pins LED1-LED4 ?

It depends entirely on the dimming levels you have set on ADIM (pin 9) AND the natural forward volt drops of the strings of LEDs. Hard to be precise of course because this circuit controls current into the LED strings and, without a detailed LED spec it's guesswork.