Re: Reported Speech
It depends where you are in terms of time.
10 am: John says "I will do it later today."
1 pm: I say "John said he would do it later today.
Three days later: John said that he would do it later that day. Did he get it done?
Jan 1: John says "I want to go to Prague this year."
June 15: John said that he wanted to go to Prague this year.
Otherwise, yes, the prior/previous day/week/month/year, or the next day/week/month/year depending on how much later it is when you say it.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.