indirect speech

[vkhu]

"If you saw my father you would recognize him at once. he is the most extraordinary-looking man." Said she

I want to change it into the following: "She told me if I had seen her father, I would have recognize him at once. He was the most extraordinary-looking man."

But I think if I do that then the first sentence would become type 3 conditional speech and the second one might mean that her father is now deceased (which might or might not be true).

So is it correct?

[5jj]

You are right about the incorrectness of your version. We can report this only as:

She told me that if I saw her father I would recognize him at once. He was/is the most extraordinary-looking man."

[vkhu]

You are right about the incorrectness of your version. We can report this only as:

She told me that if I saw her father I would recognize him at once. He was/is the most extraordinary-looking man."

So is there any kind of general rule as to when and when not to use backshift in reported speech?

[Raymott]

So is there any kind of general rule as to when and when not to use backshift in reported speech?

You can always backshift. I've found that to be a simple rule.

But you don't backshift "If you saw my father .." to "If you had seen my father ..." because 'saw' is not indicative here, it's subjunctive.
It doesn't mean "If you saw my father (literally, in the past, say yesterday)" It means something more like "If you ever see my father".

Imagine this indicative use of 'saw':
"She said 'If you saw my father yesterday, you would know he is dying.'" =>
She said that if I had seen her father the day before, I would have known (I would know) he was dying."
This is correct.

But a hypothetical "saw" remains hypothetical when you backshift it, and doesn't become "had seen".