DFW SUPVR QUESTIONS BUT DOES NOT VALIDATE THAT THE FLT CREW CROSSED RWY 35C WITHOUT A CLRNC.

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LANDED RWY 31R. GND INSTRUCTIONS WERE FOR ROMEO; FOLLOW ACR Y ON 'Y' HOLD SHORT RWY 35C. THEN GND SAID ACR X GIVE WAY TO ACR Z MD80; L TO R; CONTACT GND 121.85 OVER BRIDGE. WE CALLED BACK AND ASKED CONFIRM CLR TO CROSS RWY 35C. GND SAID YES; CONTACT GND 121.85 OVER BRIDGE. WE GAVE WAY TO MD80 ON L AND CROSSED RWY 35C. THEN SAME GND (121.65) CAME BACK AND ASKED; ACR X ARE YOU BTWN RWYS (35C AND 35L)? WE SAID YES. HE SAID HOLD SHORT RWY 35L; CONTACT TWR 126.55. WE ANSWERED ROGER; TOWER 126.55; HOLD SHORT RWY 35L. THEN TWR ASKED ACR X ARE YOU HOLDING SHORT RWY 35L? WE SAID YES. CTLR SAID; CROSS RWY 35L CONTACT GND 121.85 OVER BRIDGE. THEN SUPVR ASKED THAT WE CALL TWR WHEN AT THE GATE. SUPVR SAID WE WERE NOT CLEARED TO CROSS RWY 35C. AFTER TALKING ABOUT THIS; HE SAID THAT IT WAS NOT A BIG DEAL. HE LISTED IT AS NO FAULT NO HARM. GND CTLR'S INSTRUCTIONS WERE GIVEN AT A RATE THAT WAS TOO FAST TO UNDERSTAND AND HAD TO ASK TO REPEAT INSTRUCTIONS. TRYING TO HAVE ACFT LAND ON SAME SIDE AS GATE. WE SHOULD NOT HAVE HAD 4 FREQ CHANGES FROM RWY TO GATE. THAT IS TOO MANY AND LEADS TO CONFUSION. GND CTLRS WORKING 2 FREQ AT ONE TIME.