Also, in 2, he did say the word "to" -- he didn't articulate the "d" at the end of "found" or the "t" at the beginning of "to", but I understood him to have said both of those words.
And in "Brave to the End" I think the words were partially obscured by the music. He doesn't seem to have clearly articulated the word "the", you're correct.
In 1, I didn't hear anything unusual in either of the links you provided. "James" sounded fine to me, and anything about the pronunciation of "eyes" I would attribute to the fact that Snape is busy dying. ^_^
You're a close and careful listener, though -- that should help you in your own pronunciation! Just keep in mind there are a lot of variations in spoken English among native speakers. Good luck with your studies!
Often in spoken English, words will run together.