They all look good to me except for the second.
They denied opening my letters. = They warned, "We don`t want to open your letters."
It should be = They insisted, "We didn't open your letters."
Why? -- Well, "deny" and "warn" don't mean the same thing at all. To deny is a way of contradicting what someone else has said. When you change this to direct speech, you can't really use "deny", but it should be a verb meaning "to state something forcefully". "Warn" does not work here. In addition "opening my letters" (which they denied doing) is something that happened in the past, so in direct speech it cannot be "we don't want to ..."
Hope this helps.
Learn hard, think free!
[yes, I am an English teacher, and I *do* know
that "hard" and "free" are adjectives, rather than
adverbs, following a verb. Hey, that's the reality
of modern day English. As the Borg are so fond
of saying, "Resistance is futile."]