One point at a time.
When the word introducing the reported speech is in a past tense (said, told, thought, etc), then it is almost always correct to backshift, i.e. move the tense one step back:
"I like..." - He said that he liked ...
"I have seen her." - He told me that he had seen her
"I will try ..." - He said that he would try.
If the situation spoken of is still true at the moment of reporting, then we can backshift, but we do not have to:
"I love you." - (reported soon after:) He told me that he loves/loved me.
"We are leaving at 6.30" - (reported before 6.30:) He said that we are/were leaving at 6.30.
"Czechs drink more beer than Germans." - The guide claimed that Czechs drink/drank more beer than Germans.