There are many ways to skin this cat. To make the floating lights, I would use a particle system with Depth of Field enabled so the closer ones are more in focus. You’ll have to mess around with the settings, but to start, I would make the particles discs or faded spheres or something circular (depends on what particle plugin you are using). Turn the longevity and particle size up and birthrate down. Then make the gravity slightly negative so they float upwards. See where that gets you and keep adjusting to get the look you want.
The effect at :13 could easily be replicated with some time-remapping and keyframes for the scale, position, and rotation.