The contract should try to send its funds but it will need to have some to begin with.
You will have to send 1000000000 wei, or more when you deploy the deploy the contract. Any surplus will remain in the contract.
I can't think of any good reason to do this so I'll refrain from suggesting improvements.
Hope it helps.
WARN: I don't think anyone ...
Yes, you do need to change function Contract (... to constructor(... because this is the new way to indicate the constructor.
There is nothing else you need to do in the Factory to invoke the constructor. The constructor always runs one time on deployment, regardless of how the contract is deployed. It cannot be prevented/avoided even if you want to.