no, the thing about the dogs is, if yo fly, they'll move, if you walk, they'll stay, and then you search the area that your pokedex says there in. my problem is i haven't seen any so i can't search for them.
if you don't have suicune you can find him in cianwood city. he will be on the top of the city. then, after you met him he will run then you will fight eusine. after that he'll be below the door cave(middle between ecruteak and mahogany town). just cut down the tree and you will met him. finally you will be given a chance to catch suicune in tin tower. and for other two, potato_chips already given the answer