To me, it looks and sounds wrong to use contracted and uncontracted phrases in this sentence: "He'll know he is safe in his new home." What do you think?

It reads like colloquial conversation, and we do use contracted forms unless we wish to give emphasis:

X: He's a dope.
Y: Don't say that - he's as smart as me.
X: So you confirm it - he IS a dope!

IS = italics, but there are none on this site.

So, in your sentence, I would have expected to read:

"He'll know he's safe in his new home."