It depends a lot on the context and whether it's spoken English or more formal written English
'Did you tell me that tomorrow is Tuesday?' is possible.
but so is 'He told me that the next day was Tuesday'.
'You said that the train leaves at 10 am tomorrow morning.' is perfectly acceptable in spoken English, but if you were reporting it in written form, you'd put 'He said that the train would leave at 10am the next morning.'
Similarly for the other sentences you give -
I am going away for the weekend. - 'He told me he was going away' or 'He would be going away next weekend.'
I will not be home tomorrow night. - 'He told me he wouldn't be home the following night.'
We are going to visit him on Sunday. - 'She said that they intended to visit him on Sunday'. or 'She told me that they were going to visit him on Sunday'
They will be studying when I get home. - 'He said that he would be studying when I got home.'
She will have left when we arrive. - 'She told me that she would have left by the time we arrived.'
My father will have been working for the company for 45 years when he retires. -
This is the trickiest sentence - it's not that common to use future perfect continuous in the first place, and then turning it into reported speech!!
Most native speakers in spoken English would try to avoid a sentence like: 'He told me that his father would have been working...' . If the context allows, keep the present reference points to keep the meaning clearer -
'He told me that his father will have been working for 45 years when he retires.'
There's really too much emphasis in grammar books about reported speech - it's a bit of a red herring. There's all these complicated rules, but when we're actually speaking, we break the rules the whole time. Hope this has helped anyway. I've really got to get back to work!
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