A CE560 CAPT AS PM ALLOWED THE FP FO TO DESCEND PRIOR TO THE FAF. A GPWS TERRAIN WARNING AS WELL AS ATC LOW ALT ALERT WERE GIVEN.

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WE WERE DOING A PART 91 REPOSITIONING FLT FROM ZZZ TO HPN. I WAS THE PM SITTING IN THE L SEAT. AFTER RECEIVING MULTIPLE VECTORS AND A SPD REDUCTION; WE WERE CLRED FOR THE RNAV (GPS). WE HAD PREVIOUSLY LOADED AND BRIEFED THAT APCH. PRIOR TO REACHING BODRE; THE PF ASKED FOR GEAR DOWN; BEFORE LNDG CHKLIST. I COMPLIED WHILE THINKING TO MYSELF IT WAS A LITTLE EARLY FOR THAT ACTION. THE APCH CTLR INSTRUCTED US TO CONTACT TWR. AS I REACHED UP TO CHANGE FREQS; THE GPWS SOUNDED A TERRAIN WARNING AND A PULL UP COMMAND. IT TOOK A FEW SECONDS FOR ME TO REALIZE THE PF WAS STARTING HIS DSCNT TO MDA PRIOR TO THE FAF (CZ1MR). THE HPN TWR ADVISED US OF A LOW ALT ALERT AND TO CHK OUR ALT. THE PF CLBED BACK TO THE CORRECT ALT AND WE CONTINUED THE APCH AND LANDED. THE PF STATED HE THOUGHT WE WERE APCHING THE FAF WHEN HE CALLED FOR GEAR DOWN. THIS WAS OUR FIRST FLT TOGETHER. I SHOULD HAVE VERBALIZED MY THOUGHTS TO THE PF ABOUT PUTTING THE GEAR DOWN SO EARLY. ALTHOUGH; THE ATIS; WHICH WAS AN HR OLD; INDICATED AN OVCST CONDITION; THE SKY WAS ACTUALLY BROKEN DURING OUR DSCNT; VECTORS; AND ALL DURING THE APCH.