Restore a SQL Server 2012 backup file in SQL Server 2016/2014 I have SQL Server 2012 backup files and want to restore these to SQL Server 2016/2014. Will it work?

I need to find this out before I uninstall SQL Server 2012.
Yes this will work.  You can always go forward, you can't go backwards, at least not with backup and restore.  With older version eg SQL 2000, SQL 2005 sometimes you have to do a stepped upgrade, ie go from 2000 to 2008 to 2014, but that shouldn't be a problem for you.

Be aware when you restore your databases they will have the older database compatibility level.