The Windows Phone 8.0 SDK includes the ability to create applications for 7.1 and 8.0, so you do not need to install the 7.1 SDK.
BUT
Application development for 7.x is not supported in Visual Studio 2013.
If you need to target 7.x devices, you will need to use VS2010 or VS2012.
If you want to create o for Windows Phone 7.x, you must use Visual Studio 2012. You can install this AND Visual Studio 2013 on the same computer. The only thing you may not be able to do is to have the only solution with all the projects that you can use in both versions of VS.
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