For indirect speech, it does matter whether you use the past or present tense to 'report' what was said. If you use the past tense, it means that this action is over (in the future--when you are reporting). If you use the present tense, it means that this action is still ongoing.
So, all of these 'reports' are correct grammatically, but for a few, I offer my suggestions to keep the tense consistent:
Mark said, "I have a car. --> Mark said (that) he has a car.
Mark said, "I have never lived in this house." --> Mark said (that) he has never lived in that house.
My sister said, "I will be a doctor when I grow up." --> My sister said (that) she will be a doctor when she grows up.