This has details about installing and using LocalDB http://msdn.microsoft.com/en-us/library/hh510202.aspx
Ther are no documented restrictions I have sen on connecting to databases created before SQL2012, so you should be OK to use databases created by SQL 2008 2. However, you may not then be able to use a database file opened by LocalDB on anything earlier than SQL2012 - you need to test this yourself.
SQL 2012 LocalDB is part of the SQL Express offering, so it looks like it is free to use as described in the SQL Express licensing terms.
If you go down the route of installing a full copy of SQL Express, it is not advisable to copy the master db files to all of your instances. The SQL Express install will create its own master DB file (and files for the other system databases) and you should use the files created during the install.
Original author: SQL Server FineBuild 1-click install and best practice configuration of SQL Server 2017 2016, 2014, 2012, 2008 R2, 2008 and 2005. 1 Dec 2016
: now over 39,000 downloads.
Disclaimer: All information provided is a personal opinion that may not match reality.
Quote: "When I give food to the poor they call me a saint. When I ask why they are poor they call me a communist." - Archbishop Hélder Câmara