You can convert your existing VS 2010 database project to SSDT project by a simple right click operations. Here I have VS 2010 database project (project version SQL Server 2008). Let's have a look at the property page in VS 2010.
When you open an existing VS 2010 database project you will be prompted to upgrade the project to SSDT type. You can also launch the same wizard by right clicking on the project and selecting "Convert to SQL Server Database project..."
Post upgrade, let's have a look at the property page again.
Your existing VS 2010 database project has been converted to SSDT project. You can verify the conversion log for any errors.
How to create output from the VS 2012 database solution that can be included in a MSI installer image for installation on a client desktop that does not have VS 2012 and does not have SSDT installed on it?
You can create .SQL file as output from the VS 2012 database solution. SQL file can be included in the MSI with some level of customization.