How can I loop and blend footage end/beginning frames in After Effects?

If you are looping a property and you want it seamless, the first and last frames of the animation must be identical. The easiest way to achieve that is to copy the first keyframe, move down the timeline past the middle keyframe and then paste. Then all you need is loopOut() added to the property with the identical first and last keyframes.

If you want to loop a Timeremapped layer, the first and last frames must also be identical. If you use the "k" key to go too to the last time remapping keyframe, the Comp panel should now be blank. Use Ctrl/Cmnd + left arrow to move back one frame so you can see the last frame, set a new time remapping keyframe, press 'j' to go to the last keyframe (comp blank again), then delete the last keyframe. Again, you add a loopOut() expression, and the footage will seamlessly loop.

If you want to render a video that you can import and set to seamlessly loop using keyframe interpolation in After Effects, again, the first and last frame of the comp you are rendering must be identical, but there is one extra step you must do. Move the CTI to the outpoint of the comp so you see the last frame, but then you need to move back one frame, set the end of the work area to that frame by pressing the 'n' key, then trim the composition to the work area before you render. This time, for rendering a video that will seamlessly loop, the movie's last frame must be one frame before the animation gets to the frame that is identical to the first one.

  An easy way to check and see if you have a perfect match is to use the snapshot tool (the camera button at the bottom of the comp panel), then move to the last frame and press the Show Snapshot icon next to the Camera button. 

This has nothing to do with an expression of any fancy effects. You simply need to build a looping pre-composition where the cut happens in the middle and the end and start frames of your two duplicate layers match. This allows you to tweak whatever is in the middle with a short crossfade, a morph or overlaying a third retimed clip with feathered masking to cover up the jump.

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