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Alright, just so that you know, I am going to be answering your second question, first. Seeing as how it will take the longest to complete, and it is important to the storyline that you complete it, I will answer it first. Finding the woman's key is not that important. In order to get past the man, and into Sunyshore City, you need to have seven Gym Badges. After you obtain your Seven badges, you need to go to each of the Three Great lakes that are scattered throughout the Sinnoh Region. Upon defeating each member of Team Galactic that you see at each lake, you need to head to Team Galactics base in Veilstone City and defeat everyone there. After you defeat everyone there, you need to go inside Mount. Coronet by using the entrance that is west of Hearthome City. Make your way to the top of the mountain and defeat the Three Coomanders of Team Galactic. After that, catch Palkia. You can then go past the man, and into Sunyshore City.


The girl will just give you a little something, but I guess that it is nice to help out. You can find the key to her hotel room on the ground near where she is standing. Just search the ground on the left until you find it.


Hope this helps.

Ok,i will answer your first question the after you step out
Of the grand hotel lake there is a sidewalk it is invisible do not go up the stairs or into the house on the right it is in that area.

P.S.She will give you a lava cookie. A lava cookie heals all status problems