Your sentences are awkward and can be expressed in a more natural fashion.
You can indeed, I think, insert a remark like I think or Sally believes in the middle of a sentence as an aside or apposite, but it must be done correctly.
Here are some more natural versions of your two sentences
His parents, I think, didn't bequeath anything to him.
His parents didn't bequeath, I think, anything to him.
Note bequeath means to leave something to someone, as in a will, while inherit means to receive something from someone when they die.
Another possible structure is
His parents bequeathed, I don't think, anything to him.
But you could just say
I don't think his parents bequeathed anything to him.
He killed himself, Sally believes, yesterday.
He killed, Sally believes, himself yesterday.
Another valid structure is
Sally believes it was himself that he killed yesterday.
Or you could just say
Sally believes he killed himself yesterday.