FLT CREW OF A320 INADVERTENTLY READ BACK CLRNC FOR ACR FLT WITH SIMILAR CALL SIGN AND BEGAN DSCNT WITHOUT CLRNC.

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NEAR MAGOO INTXN; ZAU STARTED ACFT ON A DSCNT TO FL350; THEN FL330; THEN FL290; THEN FL270. CAPT WAS PNF. FO WAS PF. ACFT SPD WAS THEN SLOWED BY ATC; THEN ACFT WAS PLACED ON A RADAR VECTOR. AT FL270; CAPT SWITCHED TO COM #2 TO GET ATIS AND TO CALL GND HANDLER FOR GATE INFO. FO/PF WAS GIVEN COM #1 FOR ATC. DURING THIS TIME; FO/PF STARTED DSCNT TO FL240; STATING THIS WAS GIVEN BY ATC. CAPT/PNF DID NOT HEAR THIS EXCHANGE WHILE ON COM #2. CAPT/PNF RETURNED TO COM #1. AT FL250; ATC CALLED SAYING ACFT WAS BELOW ASSIGNED ALT. CAPT/PNF STATED WE WERE ASSIGNED FL240 AND WERE ON ASSIGNED HDG. ATC STATED ACFT SHOULD BE AT HIGHER ALT. ATC THEN GAVE ACFT FL250; AND SWITCHED ACFT TO ANOTHER FREQ. NEXT ATC FREQ ADVISED ACFT OF POSSIBLE PLTDEV. ACFT CONTINUED TO ORD. FACTORS: FO/PF NEW TO ACFT TYPE; BUT EXPERIENCED. ACFT AHEAD HAD SIMILAR FLT NUMBER. MULTIPLE ALT; HDG; AND SPD CHANGES IN SHORT PERIOD. 2 MAN FLT DECK. NEED FOR PNF TO LEAVE ATC FREQ TO MAKE COMPANY CALLS AND UPDATE ATIS INFO. ACFT VECTORED OFF OF ESTABLISHED ARR PROC. SPD AND ALT NUMBERS SIMILAR; IE; SPD 270 KTS; FL270. SUPPLEMENTAL INFO FROM ACN 574186: FLT WAS ON RADAR VECTORS; HDG CHANGES AND DSCNT FROM FL330 TO FL270. THE CTLR SAID THAT THE DSCNT WAS FOR ACR Y. I WAS NEVER TOLD ABOUT ACR Y AS A FLT NUMBER CONFLICT. THE CTLR ALSO SOUNDED UNCERTAIN OF WHAT DIRECTIONS SHE HAD GIVEN ME.