The bigger trick is, you have to genetically breed your surrogate species (elephant) until you have a mother that won't reject the fetus. They basically need to genetically transition an elephant to a mammoth over several generations. Personally, I have no issues with the undertaking, but would rather they first focus on endangered species.
I own an island off the coast of Costa Rica. A sort of...biological preserve, make the one they've got down in Kenya look like a petting zoo.
You're thinking of a mastodon -- a mammoth fro ain't no reason to say no. Advances in Dark and Lovely technology would make the mammoth fro an insignificant risk.
They can't; one article I read on this topic said that all that remained of the dinosaurs were fossil remains.
They didn't die out until 10K years ago. Right around the appearance of hungry dudes with sticks and nets. Feel free to believe the cartoon though.