1. Install the Windows Mobile 6.5 Developer Tool Kit (DTK)
This is the most critical step. The DTK contains the emulators, libraries, and framework versions needed to develop for Windows Embedded Handheld 6.5.
Download: You need to download and install the Windows Mobile 6.5 Developer Tool Kit. You can typically find this by searching for msi files named WindowsMobile65DeveloperToolKit.msi
Installation: Run the installer. It will integrate with your existing Visual Studio 2008 installation, adding new project types and, most importantly, the correct emulators.
2. Select the Correct Emulator in Visual Studio
Once the DTK is installed, you will have new options in your deployment device list.
In Visual Studio, when you go to deploy your application (as seen in your second screenshot), the device list should now contain entries like "Windows Mobile 6.5 Professional Emulator" or "Windows Mobile 6.5 Classic Emulator"
Choose the WEH 6.5 emulator, not the Pocket PC 2003 one. These newer emulator images come with the .NET Compact Framework 3.5 (which is backward compatible with 2.0) pre-installed, which will resolve your ".NET Compact Framework v2.0 could not be found" error
3. Why Your Other Attempts Failed
.NET CF 2.0 Error: The base "Pocket PC 2003" emulator image is a clean OS without the .NET runtime. Your app needs it, so the deployment fails. Using the correct WM 6.5 emulator solves this
Upgrade Patch Error: The "upgrade patch" error occurs because you were likely trying to install a Service Pack or update for the .NET Compact Framework 2.0 SDK on your computer, but the base version of that SDK was not installed. Installing the full WM 6.5 DTK is the correct approach