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No instead there are three Sonic titles under the name of Sonic Advance, Sonic Advance 2, and Sonic Advance 3.
No as Sonic Advance 2 came out after Sonic Adventure 2 Battle and Sonic Adventure 2 Battle was only made to be compatible with Sonic Advance.
No, only sonic advance
Sonic Adventure
Sonic Adventure 2: Battle
Sonic Advance
Sonic Advance 2
Sonic Advance 3
Shadow the Hedgehog
She doesn't exist until Sonic Advance 2.