I recently recorded a five hour Introduction to Extended Events course on Pluralsight that answers every question that you ask here:

SQL Server:Introduction to Extended Events

If you need data to be persisted when the event session is stopped you have two options, use the file target, or read the data from the target into a table before stopping the session. If you are using an in-memory target, you can drop all of the events from the event session to stop data collection, and then query the target data as necessary from the DMVs.

Unless you are on 2012, using Extended Events for general troubleshooting doesn't make sense over using SQL Trace because it doesn't expose enough information in 2008. There are more advanced diagnostic and troubleshooting scenarios in 2008 where Extended Events can help with solving complex problems, but most scenarios Trace still makes the most sense in 2008.

If you are new to Extended Events, and on SQL Server 2008/2008R2, download the SSMS Addin for SQL Server 2008 that I wrote and it will help you with using the feature better. In SQL 2012, there is a built-in UI in SSMS already.

Beyond this, read the posts in my blog category for Extended Events, I've written over 300 pages of content the last four years on the topic, and the answers to your questions have been covered in that content as well.