2010 LEXUS ES Electrical System Problems

I BEGAN TO NOTICE AFTER LONG DRIVES, A SMELL SIMILAR TO A CAR OVERHEATING. ONE NIGHT, WHILE WARMING THE CAR UP, THE ALTERNATOR LIGHT CAME ON (THE BATTERY SYMBOL). I FIGURED IT WAS PROBABLY MY BATTERY AND DECIDED TO CALL AN UBER. IN THE SHORT TIME THAT I WAITED FOR MY RIDE, THE CAR BEGAN TO SMOKE. THE NEXT MORNING I TOOK THE CAR TO MY MECHANIC AND HE DISCOVERED THAT ENGINE OIL WAS LEAKING FROM THE VALVE COVER GASKETS DOWN INTO THE ALTERNATOR CAUSING AN ELECTRICAL SHORT CIRCUT.

I HAVE LEXUS ES350 YEAR 2010 ,I HAVE PROBLEM WITH THE BATTERY NEED TO JUMP STAR I BRING TO THE DEALER TO CHECK ,THEY TOLD ME NEED TO CHANGE THE BATTERY ,WITH THE FULL PRICE $198.00 ,THEY TOLD ME THE BATTERY ON MY CAR IS NO MORE WARRANTY I HAVE NO IDEA ,BUT THE BATTERY ON MY CAR FROM LEXUS LOGO AND WITH THE 84 MONTH WARRANTY ON IT , IF YOU COUNTING BACK ON THE CAR 2010 UNTIL NOW IS NOT 60 MONTH YET , BUT THE TOLD ME NO MORE WARRANTY ,THEY SAY THE LEXUS COMPANY ONLY WARRANTY FOR 2 YEARS I HAVE TAKE THE PICTURE ON THAT BATTERY THEY HAVE PART NO.# 00544-MF24F-575 575CCA/130RC 84 MONTH WARRANTY LEXUS LOGO DISTRIBUTED BY TOYOTA MOTOR THE SERIAL # 2111278637 PLEASE CAN YOU TELL ME IS THAT STILL WARRANTY OR NOT , AND WHAT DO I HAVE TO DO NEXT...