How many transaction can I broadcast simultaneously?
You need to wait for the transactions to be confirmed in a block. The limit is on the number of unconfirmed transactions that can be chained together and is completely unrelated to how quickly the transactions were received.

The chain can only be extended once the unconfirmed transaction chain shrinks, and that can only happen as transactions are confirmed. It is important to note that the entire chain may not be confirmed in the same block and that the next block may not include any transactions in the chain of unconfirmed transactions.