>Can multiple streams write to a Delta table at the same time?

Yes delta uses optimistic concurrency control and configurable isolation levels

>I'm concerned there could be conflicts but I'm not sure how Delta would handle it.

Write operations can result in conflicts depending on the isolation level and could raise an exception. For more details on the types of exceptions and how to handle them - see https://docs.databricks.com/delta/concurrency-control.html#conflict-exceptions