How to fade in/apply transition as a node in Fusion to image in Davinci Resolve?
There are many ways fade in/out the opacity of a clip in Fusion, and which method you choose depends on your needs.

If, your composition only contains one MediaIn node, and you want the actual compositing to occur outside the Fusion page (to keep your edit flexible, for instance), then a simple method is to use a brightness/contrast node, and animate the Gain slider between zero and one.  Make sure the R, G, B, and A channels are all included in the operation by enabling the corresponding boxes at the top of the inspector.  The Alpha (A) channel is particularly important, as it is the property which controls the extent to which the colors of pixels mix when they are superimposed.  As an exercise, try disabling the R, G, and B channels, and animating A to see the difference between Alpha and Color contribution.  You'll see that Alpha isn't the same as the “opacity” slider in other areas of the Resolve interface.

In another case, suppose you have two media sources inside your Fusion composition, and you want to layer them together and animate a transition from one to the other.  A convenient way to accomplish this is included in the Merge node that you'd need to use to combine the images anyway.  However, if you try moving the alpha gain slider down, the results might not be what you expect.  You'll notice that the results of this action look exactly like the example above, where you only affected the alpha gain channel in the B/C node.  To get the Merge node to affect the R, G, and B channels as well as Alpha, you need to slide the Additive/Subtractive slider over to Subtractive.

Hope this helps.