FLC OF A B757 RECEIVED PUSHBACK FROM GATE ONTO AN ACTIVE TXWY WITHOUT CLRNC FROM TWR. IN ADDITION; CAPT FAILED TO FOLLOW NOISE ABATEMENT PROCS AFTER TKOF BY TURNING TOO EARLY.

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AFTER A MECHANICAL DELAY TO CHK FOR THE SOURCE OF SMOKE IN COCKPIT AFTER LNDG (NOTHING FOUND); ACFT DEICING; CHANGE OF RWY; AND NO HEADSETS FOR GND PUSHBACK PERSONNEL; THERE WAS SOME CONFUSION AS TO THE PUSHBACK PROCS AND THE ACFT WAS PUSHED BACK ONTO AN ACTIVE TXWY WITHOUT CLRNC. THE BASIC PROB REALLY STARTED WHEN WE WERE INSTRUCTED THAT THE ACFT WOULD BE PUSHED APPROX 10 FT TO BE DEICED. THIS WAS COORDINATED WITH THE RAMP TWR (131.85). AT THE LAST MIN; WE WERE TOLD THAT DEICING WOULD BE DONE AT THE GATE. WHEN THE DEICING WAS COMPLETED AND CONFIRMED OVER THE RADIO I RECEIVED HAND SIGNALS FROM THE GND INDICATING THAT THE HEADSETS WERE NOT WORKING AND THAT I SHOULD RELEASE MY BRAKES. AS WE PUSHED BACK I COULD SEE NO ONE ON THE TUG OR ON THE GND. THIS WAS VERY DISCONCERTING BUT WE DID NOT SEEM TO BE PUSHING BACK VERY FAR. I DID NOT REALIZE THAT WE WOULD BE OUT OF OUR RAMP CTL AND I THOUGHT THAT SINCE I HAD CALLED GND WHEN WE WERE DEICING TO ASK FOR RWY 4 (L OR R) THAT WE WERE CLRED TO PUSH AND WOULD CONTACT THEM TO TAXI. AS WE STOPPED OUR PUSH WE WERE CONTACTED BY GND AND TOLD 'IN THE FUTURE TO CONTACT THEM PRIOR TO PUSHING ONTO AN ACTIVE TXWY.' I APOLOGIZED AND WE STARTED TAXIING TO THE RWY WITH CLRNC FROM GND. THIS WAS THE FIRST TIME I REALIZED THAT THE TAIL HAD INTRUDED ONTO THE TXWY. WE HAD A MINOR PROB WITH STARTING THE SECOND ENG AND AS WE STARTED TOWARD THE RWY WE WERE CLRED FOR TKOF. BECAUSE OF AN ACFT ON THE APCH AND THE ADMONITION THAT IF WE COULD NOT GET OFF QUICKLY WE WOULD BE AWHILE; WE COMPLETED ALL CHKLISTS BUT WE HURRIED THROUGH THEM. WHEN IT GOT TO TKOF BRIEFING I BRIEFED AND FLEW THE CLBOUT TO 5000 FT; 090 DEG HDG; AFTER TKOF ETC. UNFORTUNATELY; I DID NOT NOTICE THE 4 DME NOTE AND TURNED A LITTLE EARLY. THE CTLR ASKED OUR HEADING WHEN WE TURNED (090 DEGS) AND TOLD US ABOUT THE 4 DME TURN FOR NOISE ABATEMENT. HE STATED THAT THERE WAS NO PROB BUT IN THE FUTURE WAIT UNTIL 4 DME TO START THE TURN.