[Grammar] He is and he was

[Checkmate]

"He said he was an engineer"

I'd say it's right but it sounds like he's not an engineer.

Could I say "He said he is an engineer" or "He says he is an engineer"

 

[MikeNewYork]

Yes you could. The tense backshift is optional there.

 

[Checkmate]

Yes you could. The tense backshift is optional there.

Which one could I say? "He says he is going" or "He said he is going"

 

[MikeNewYork]

In reported speech,"said" would more common, unless the speech was very recent.

 

[Matthew Wai]

'He just said to me over the phone that he is going dancing tonight.'
The phone call might be just a few seconds ago, very recent. Could 'said' still be used?

Not a teacher.

 

[MikeNewYork]

Yes. But "says" could also be used.

 

[Checkmate]

Yes. But "says" could also be used.

"The website says dinasours exist"
"The book says Science is important"

Could I use "says" for a speech that has been written and still able to be read?

 

[tedmc]

Yes, even entire stories(narratives) can be written in the present tense.
The present tense gives the sense of reality and immediacy.

not a teacher

 

[Matthew Wai]

"The website says dinasours exist"
"The book says Science is important"

Whenever you read the website/the book, it always says so, such is a repeated action in the present, so the simple present can be used.

Not a teacher.

 

[MikeNewYork]

Absolutely. If something said/written in the past is still true, the present tense can be used. In both of your sentnces, the past tense could also be used.