AN MD11 LEVEL 2 - FUEL QTY/USED CHK ALERT ANNUNCIATED. WHILE HANDLING THIS ABNORMALITY; THE CREW BECAME TASK SATURATED AND BEGAN A CLB TOO EARLY.

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AFTER DEPARTING ZZZZ ENRTE TO ZZZ; WE REQUESTED OUR OCEANIC CLRNC VIA ACARS. WHILE WAITING FOR OUR RESPONSE; WE GOT A LEVEL 2 -- FUEL QUANTITY/USED CHK ALERT. I INSTRUCTED THE FO TO CONTINUE FLYING AND TALKING WHILE THE RELIEF PLT AND I RAN THE EMER PROC RED TABS. WE RAN THE CHKLIST. THE CHKLIST IS MEANT TO DETERMINE IF THERE IS A FUEL LEAK OR A FUEL QUANTITY INDICATING ISSUE. IT ALSO CALLS FOR A TURN-BACK IN CASE OF AN ACTUAL FUEL LEAK. THE CHKLIST LEAVES THE FUEL SYS IN MANUAL WITH NO GUIDANCE ON HOW TO HANDLE TAIL FUEL; WHICH WE HAD. THE CHKLIST IS CONFUSING AND I QUESTIONED WHAT HAPPENS TO OUR TAIL FUEL. SINCE I HAD CONCERNS ABOUT THE TAIL FUEL; THE RELIEF PLT AND I READ THROUGH THE CHKLIST AGAIN TO DETERMINE IF WE HAD OVERLOOKED ANYTHING. WE FINISHED REVIEWING THE CHKLIST FOR THE SECOND TIME AND MONITORED THE FUEL USAGE TO DETERMINE IF THERE WAS A FUEL LEAK. THE RELIEF PLT AND I BOTH AGREED THAT THERE WAS NO FUEL LEAK NOR WAS THERE AN INDICATING PROB. I WAS STILL CONCERNED ABOUT TAIL FUEL AND TAIL FUEL MGMNT (AUTOMATIC DISTRIBUTION OF FUEL FOR OPTIMUM CTR OF GRAVITY AND FUEL BURN). CONSIDERING OUR RE-RELEASE FLT PLAN AND A DELAYED TKOF FROM ZZZZ; I DECIDED TO RETURN THE FUEL SYS TO AUTO; TO RESET THE FUEL SYS CONTROLLER ALLOWING THE AUTO MODE TO FUNCTION NORMALLY AND PROVIDE FOR TFM. THE FUEL SYS APPEARED TO WORK NORMALLY IN THE AUTO MODE. WE THEN RECEIVED AN ACARS MESSAGE THAT REQUIRED US TO CONTACT OCEANIC CLRNC CTL VIA VOICE FOR OUR OCEANIC CLRNC. RETRIEVING THE CORRECT FREQ; I THEN CONTACTED OCEANIC CTL ENSURING THAT THE FO AND RELIEF PLT WERE BOTH MONITORING RADIO #2 ON XXX.XX (THE FO WAS ALSO MONITORING RADIO #1). WHILE WE WERE WAITING FOR OUR CLRNC; WE GOT THE SAME LEVEL 2 -- FUEL QUANTITY/USED CHK ALERT. THE RELIEF PLT AND I BEGAN RUNNING THE CHKLIST AGAIN AND 1/2 WAY THROUGH THE CHKLIST OCEANIC CTL CAME BACK WITH OUR CLRNC. WE STOPPED OUR FUEL QUANTITY/USED CHK CHKLIST AND FINISHED COPYING AND READING BACK OUR OCEANIC CLRNC. THE OCEANIC CLRNC CALLED FOR AN ALT AND TIME CONSTRAINT AT ZZZZZ INTXN. AFTER READING BACK THE CLRNC AND VERIFYING THE XING POINTS IN THE MCDU (FMS); THE RELIEF PLT AND I CONTINUED WITH THE FUEL QUANTITY/USED CHK CHKLIST WHILE THE FO CORRECTLY LOADED THE MCDU WITH THE TIME (XA43+) AND ALT (FL320) CONSTRAINTS AT ZZZZZ INTXN. WE ARE LEVEL AT FL300 AT THIS TIME. TRYING TO STAY 'IN THE LOOP;' THE RELIEF PLT LOOKED UP AND QUESTIONED THE FO IF WE SHOULD PUT FL320 IN THE FCP. THE FO AND I AGREED TO PUT FL320 IN THE FCP. MY THINKING WAS THAT SINCE THE ALTS AND TIME CONSTRAINTS WERE LARGE FONTED (HARD TUNED); PUTTING FL320 IN THE FCP WOULD PRESELECT THE ALT AND SERVE AS A REMINDER FOR A LATER CLB. SHORTLY AFTER SELECTING FL320; THE ACFT BEGAN A CLB; I VERBALIZED THAT WE'RE CLBING AS THE ACFT LEAVES FL300. GETTING DISTR WITH THE RED TABS; I NEVER SWITCHED BACK TO RADIO #1 AND DIDN'T HEAR THE CONVERSATION THAT THE FO IMMEDIATELY BEGAN HAVING WITH DOMESTIC CTL. THE FO CONVERSED WITH DOMESTIC CTL AND TOLD US; AFTER THE FACT; OF WHAT WAS SAID BTWN THEM. HE SAID THAT AS THE ACFT STARTED CLBING AND WAS PASSING FL303; HE TOLD DOMESTIC THAT WE WERE OUT OF FL300 FOR FL320. DOMESTIC CTL STATED THAT WE WEREN'T CLRED TO FL320 AND THE FO QUICKLY RESPONDED THAT WE'LL DSND BACK TO FL300; AT WHICH TIME DOMESTIC CTL CLRED US TO FL320 AND SAID THAT WE NEEDED TO MAKE SURE THAT THE NEXT TIME WE HAD CLRNC (FROM HIM) TO CLB AND THAT THERE WAS NO PROB (AT THIS TIME). WE COMPLIED WITH THE CLB CLRNC AND LEVELED OFF AT FL320.