I think unfortunately you have misunderstood how AE assembles a preview, what you're experiencing is normal. AE builds each frame, with all the effects into the RAM - when that frame is done, it goes green. This process is a lot slower than an editing program which as far as I know, playback the original files from one edit point to the next. Sometimes when previewing from the RAM, AE will not be able to keep up (other background processes sharing RAM etc...) so it sort of stumbles.
If you open the Preview Panel, you can see lots of options for the types of preview you want and these are customisable. So you can decide to playback without audio, playback from the current time indicator etc...
I also make a lot of use of the Solo controls to only preview the layers I am currently checking. AE isn't an editor so if you need to set timing, you should do that in PP first, then add your effects in AE.
I'm not a native speaker, so I guess I didn't make it clear enough, sorry for that.
I'm not a new AE user, I've been working with it for years now.
The problem is the priority of actions that After Effects does.
It should preview first and pre-render the further part when it has some spare power, so it can preview longer in real time.
In my case it was doing things the other way around - it prioritized the pre-render over preview and if there was any non-green part in the timeline, the preview would be slow, even if it was green and should be in real time.
While I was writing this reply, I thought of disabling multi-frame rendering and it feels like it solved the problem.
I have to test it more to be sure, but for now it seems to be ok.