Also good :)

With a slingshot maneuver, why does the the direction of the inertia change though? If you zoom out far enough the lines are mostly parallel with a "dip" where there as mass. Why can an object enter parallel to a line, be dragged with the line towards the mass, miss it and exit on a path not aligned with a line? https://i.imgur.com/qj8fafd.png

That's a screenshot of an animation where the grid is moving. The lines don't capture the object. They just nudge it a bit. Kind of like a ball rolling across a treadmill.

Also that image doesn't show the slight twist in the grid caused by the earth's rotation. Another part of the video does though.

You can only slingshot in a direction another body is orbiting (to gain velocity). You're harvesting it's momentum, basically!

Not sure if the term itself restricts it to an accelerating maneuver, but of course you can do the reverse and slow down.

The more I try to read about this the more unsure I am I truly understand it, so perhaps not...