I have ArcGIS 10.3 loaded with the 10.3 developer kit that I use with Visual Studio 2013. If I also have Visual Studio 2010 loaded, can I load the 10.2 developer kit alongside the 10.3 version and use it with VS2010?
Do you mean that you have ArcGIS for Desktop, Engine, or Server 10.3 installed with the ArcObjects SDK 10.3? If so, you would not be able to install version 10.2 of the developer kit because these products do not allow side-by-side installs.
Yes, I have ArcGIS for Desktop 10.3 loaded with the ArcObjects SDK 10.3. Your answer suggests that the SDK is not standalone, but rather relies on some components that are installed with the version of the desktop software a user has -- is that correct? I was thinking/hoping that the SDKs were standalone.
The ArcObjects SDK requires that you have one of the following software installed
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