Is there a way to create a series of motion paths (out of empty game objects) for camera animation and smoothly lerp, both transition and rotation, between them? What kind of math would be involved in that?
There are a lot of asset for this in the AssetStore, incuding free. One of the most popular is iTween (https://www.assetstore.unity3d.com/#/content/84), I think. See it's demos, I hope this is what you need.