Scanning on a number line

Setting up things with expressions would still require separate compositions for each segment, so you save nothing there. All the expressions can do is give you a bit of convenience for calculating the number increments and spacing based on slider controls. You would build a prototype comp which has the setup within and then you can just duplicate it and modify the sliders. Scripts like this can of course set you up, too:

https://aescripts.com/easyrulers/

That would then also facilitate animation. Once you have a working comp, you could duplicate it and just replace the assets on the timeline with the different segment or you use animation presets and adjustment layers which you can easily re-apply or copy & paste. A million ways to do it and it certainly isn't hard to do, especially since the example you provided looks rather trivial. you just have to be strategic about it and understand soem of these concepts in AE, which is probably the hurdle here, so I'd strongly advise to read the online help based on all the confusing magic words I mentioned and look up a few tutorials.

Mylenium

In your case you'd basically create each relevant timeline segment in a pre-composition which you then drop into the main composition and then duplicate and trim it into your three animation steps so you don't have to put up with too many animation keyframes. Then it's all just a case of animating soem basic position and scale parameters and the effects parameters where relevant. Rinse-repeat for every of your 20 segments.

Mylenium

Timeline setups and diagrams typically involve expressions to auto-increment values and space out elements evenly if you really don't want to do it manually. Whether that's worth rigging up entirely depends on how big a project we're talking about. Makes no sense to get into any of that if we're only talking a handful of values. You'd have to be much more specific about that and show us your design concept and explain what you actualyl need. Similarly, swish wipes/ swish zooms are all an illusion. The timeline could in fact not even exist as a whole, just sections of it that are transitioned when everything is blurry and moving fast and even that is a very relative term. Since there is no way to calculate such extreme motion blur, most of these setups make exrtensive use of directional and radial/ zoom blur effects to create the perception of speed rather than actually animating things so fast. the rest is then just tweaking the timing. I couldn't find an example of the series, so I can't advise specifically, but this is the basic drill for these kinds of things.

Mylenium