Deoxys's stats will change when traded; each game has different base stat values and movepools for Deoxys, which are recalculated when traded. Remember RBY's Time Capsule? This works the same way. Also note, that unless the Deoxys was caught at Birth Island, you CANNOT trade it.

As for the dogs, they only appear on mainland Kanto, not the islands 1-7. I've made a post in this thread that covers a lot of the points for dog hunting; you can read up on that. Quite a few other people have made good points as well.

Raaah. I have a few nice Pokemon that I'd like to have migrate to Platinum but they know HMs. I tried breeding them but they recieved the HMs as Egg Moves. Is there any move deleter in FR/LG?

You find the Move Deleter in Fuschia City (the one with Koga). IIRC, it was the house to the right of the Pokémon Center.