In most of your sentences, past and present tense are both fine. E.g.:
He said this in his letters.
This is fine, because he wrote the letter in the past.
He says this in his letters.
Even though he died 100 years ago, he still speaks through his letters, so this is also fine.
Be careful with this one:
He himself appeared in a film about his life.
This is okay, but only because the verb appear can mean to take part in a film/movie, play, television programme, etc.
The only one I consider wrong is:
* In this photo he looked healthy.
If you want to use the past tense, you should use appear.
When you say he looks healthy the focus is on you, and your experience. Your experience is happening now, so use the present tense.
When you say he appears / appeared healthy the focus is on him. He appeared healthy at the time the photo was taken and, because the photo has not changed, he still appears healthy now.
In this photo he looks healthy.
In this photo he appears healthy.
In this photo he looked healthy.
In this photo he appeared healthy.
Barrie England points out that, in certain contexts, “In this photo he looked healthy.” is fine. The sense is something like, “As you can see in this photo, he looked healthy in 2000.”