You cannot catch Rotom in HeartGold or SoulSiver, you must trade it from a Diamond, Pearl or Platinum game.
PS. If you put Rotom at the front of your party, you can go to the basement of Silph Co in Saffron City. If you examine the items, Rotom will change form.
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No. You can only catch Rotom once.
There is no specific ball needed to catch Rotom, use whichever ball you want.
No you do not have to use a cheating device such as an Action Replay or a GameShark in order to change Rotom into any of his other forms in Pokemon SoulSilver since there is a way to change it into its various forms in SoulSilver, you will need to place Rotom as your lead Pokemon and then you will need to operate the elevator that can be found in Silph Co. of which can be found in Saffron City in the Kanto region and when the elevator stops you can find the appliances that will allow Rotom to change into Fan Rotom, Frost Rotom, Mow Rotom, Heat Rotom or Wash Rotom.
bring rotom and make sure he is first and go in the elevator and you will see rotom forms
No, you can not catch Phanpy in SoulSilver. It is a version exclusive to HeartGold.