You can't get Clair's number until after you do the double battle with her and Lance which occurs in the Dragon's Den after you have defeated your Rival in Mt. Moon. Once that occurs, Clair leaves her Gym daily between 6 AM and 10 AM. You can find her in the Dragon's Den. Once you talk to her she'll give you her number and disappear.
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In between 6:00 and 10:00 game time, go to the dragon's den after you've beaten her and Lance with your Rival. She'll be off to the side, so go talk to her. She'll give you her number.
after you and your rival have beaten her and lance in a tag battle, she will be in dragon's den between 6 and 10 am
There is no best Pokemon on Pokemon HeartGold.
there is no Pokemon Mansion in Heartgold.
They are not in Pokemon HeartGold
No, but you can trade Pokemon only in HeartGold to Black