The Twin token enters as an untapped attacking creature. It's not subject to any costs to attack or restrictions on attacking.

The Twin token won't trigger any abilities that trigger "when [a creature] attacks."

The token's power and toughness are set equal to Gemini Engine's power and toughness. If there's a Glorious Anthem on the battlefield (which gives your creatures +1/+1), Gemini Engine is 4/5. The Twin token starts as a 4/5, and then the Anthem gives it +1/+1, making the Twin a 5/6 creature.

Once the token has been created, its power and toughness aren't dependent on Gemini Engine's power and toughness, and they won't change if Gemini Engine's power and toughness change.