Thank you for using just answer.
I believe you are referring to the battery warning light and the coolant level warning light here.
The battery warning light comes on anytime voltage falls low. You stated you just had the battery replaced- be sure that the connections are clean and tight, the battery needs to be tested to be sure that it's 100% charged and good, you then need to have the alternator tested. Usually when this light comes on this is a forewarning of alternator failure.
As far as coolant level indicator, you need to check your coolant level, you could possibly have a leak here, it would need to be visually inspected and pressure tested to verify. Water pumps and radiators love to leak on these cars.
ASE Certified Technician
ASE Certified, 10+ years experience, Lexus and Toyota Certified