Battle 1 has to go to Lugia. It is true that Dragonite has multi-scale, however, Lugia also has that hidden ability, so that makes it null. In addition, while Dragonite has a high attack power, Lugia also has a high defense to be able to tank his moves, and to make it worse for Dragonite, Lugia is faster, so he can strike first before Dragonite, and don't think Dragonite can use special attacks, because Lugia has an even higher dpecial defense than his defense, along with an advantage in HP. He also has moves to counteract Dragonite, like Calm mind and reflect. I'm sorry, but this can only go to Lugia.
Battle 2 is much closer. Archeops is faster and has insane attack power, so he can strike first, however, if that doesn't one hit, Yvetal can destroy him with his high special attack and Archeop's low special defense. Also, if Archeops gets below 50% health, his ability makes it so his attack and special attack is halved, so if he get's below 50%, Archeops is screwed. However, Archeops can instantly kill with Head smash, and although it has a lesser accuracy, i'm gonna bet on the fact that it will hit and Archeops will win.