There's an index.refresh_interval setting. It defaults to 1s, so by default your data will be available for querying within one second after being indexed.
In general, yes. But keep in mind that the Elasticsearch JVM GC could fire up right after the document is indexed and possibly run for a few seconds if there is a lot of memory pressure. When the GC is done Elasticsearch will continue to process queries but it may be the indexed data hasn't been refreshed yet. So, a query run "1 second" after the index operation may not in fact return the document. However, this would be a very rare case.