The reason for this is that visual studio only copies resources to the output folder if Copy Local is set. Just set the reference to Copy Local and you should be fine.
Check out this link on how this works.
When you reference ProjectA, the references from ProjectB is not automatically referenced. For this to work, you need to add a reference to ThirdParty.dll from ProjectA as well if you only use it in XAML. The compiler does not copy references that are only used in XAML. But if you use them in code, they are copied.
This is the same issue as discussed here
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