1) Yes, the data goes into a transaction which goes into a block that every node receives. If it's off-chain stream data, only the data hash (and some other metadata) goes into the transaction and rest is delivered off-chain.
2) In 1.0 or 2.0 a single transaction can publish one item to each of multiple streams. In 2.0 a single transaction can publish multiple items to a single stream. An example would be where the stream is collecting events, and multiple events are recorded simultaneously and atomically in a single transaction.
3) Any problem experienced by a particular node does not affect the rest of the network, unless the network is dependent specifically on that node functioning.