Queries on database migration
I did small tests Database compatibility level remains the same.

1.Created dummy database on 2008r2
2.Restored it on 2012

So while restoring,i could see version being changed,but after restoring compatability level remained the same.So you need to alter database to 110 compatibility level to get benefits of SQL 2012

Database 'backupdb' running the upgrade step from version 699 to version 700.
Database 'backupdb' running the upgrade step from version 700 to version 701.
Database 'backupdb' running the upgrade step from version 701 to version 702.
Database 'backupdb' running the upgrade step from version 702 to version 703.
Database 'backupdb' running the upgrade step from version 703 to version 704.
Database 'backupdb' running the upgrade step from version 704 to version 705.
Database 'backupdb' running the upgrade step from version 705 to version 706.


From Paul Randal Q&amp;A sessions,Nakul blogs,below are the details of version.

These file versions are the internal storage format, and have nothing to do with the compatibility level of the database

http://beyondrelational.com/modules/2/blogs/77/Posts/19759/0311-sql-server-database-files-upgraded-from-version-nnnn-to-mmm-why-databases-cannot-be-restored-ba.aspx

For second question,i would recommend running the database upgrade advisor,please see below link for more details

https://technet.microsoft.com/en-us/library/ms144256(v=sql.110).aspx

http://beyondrelational.com/modules/2/blogs/77/Posts/19759/0311-sql-server-database-files-upgraded-from-version-nnnn-to-mmm-why-databases-cannot-be-restored-ba.aspx