I tested Hyperlapse with Action 2. It was my first time ever doing a hyperlapse. I used 4K and Auto, and it looks like the frame rate is automatically set to 30 fps, without any possibility to choose another frame rate. Any possibility to get 60 fps in camera?

Another question: how are these hyperlapse actually acquired by the camera? Is it taking many pics and put them together in a video clip and then deleting the pics, all that in camera?

Then I think we could we get a similar result by running a Timelapse and then arranging by ourselves the timeline of the pics with a custom program or soft?
Thanks.  

If you import your hyperlapse clip into a 60 fps timeline, you get 60 fps and it will go twice as fast.

About second question, yes you can just put it on timelapse and get the images yourself, but hyperlapse-function in camera is to make it easier (faster) in post.
When I want full control over the result, I use timelapse. But most times hyperlapse works good enough + less work after.

Thanks for the info.
I suppose if we can record a GPS track with adequate data rate in parallel with a timelapse, an adaptive hyperlapse can be created, with some programing...

Just to conclude on this, Action 2 minimum interval time for timelapse is 0.5 s. This is still too long for most hyperlapses. It would be ok only for slow motions, like walking slowly maybe. Also, I checked that timelapse would take mostly blurry pics while jogging, making it unusable for building a hyperlapse in post.
hyperlapses uses much shorter acquisition times than for typical pics, making more suitable for situations with lots of motions.