You are mixing up a lot of things:
Google Mobile Services (GMS) as well as all the other Google apps and services are not part of Android Open Source Project (ASOP), therefore using AOSP you will never get them.
What is the used system for providing OTA updates?
AOSP is source code. You can clone it using Git/Gerrit to clone the source code repositories - thats it (and then use it to develop an own version for your device). OTA updates are provided by Google for Google Smartphones. The same is true for any other vendors selling Android Smartphones (if they provide updates at all).
Every device gets it's very specific update. Update by Google are useless for any other device.
I heard about Google providing updates for only 3 years so we need to adopt next major update during 3 years, is it true?
That is true for Smartphone Android versions. I can't find the source but AFAIR Google is providing patches for the AOSP source code for more than three years.
What are the faced difficulties / challenges?
For you the largest challenge is to understand that Android is not an OS like Windows. There are no general OS that can be installed on different device types, there are no binary releases, no binary updates, just the source code without device drivers, ...
Any other subjects?
As it turns out that originally you want to develop an own ROM please use https://stackoverflow.com for further questions as developing question are off-topic here.