What’s the maximum number of slots for a multi-tool

The odds are actually pretty high that you will eventually "meet" somebody, as you can see. The odds of you being on the same planet at the same time and in the same place are where the odds drop like a rock unless you put in the effort and materials.

This is actually a version of the Birthday Paradox. With enough people involved the odds of two people having seen the same planet goes up VERY quickly.

As far as I know, Atlas Stones can be received from Atlas Stations you find along your exploration. You can find them randomly, or they will likely be on your specific path to the center of the universe.

As to getting them randomly from around the systems and planets, I want to say no. However, you can buy them from some traders, albeit extremely overpriced (5+ Million Units).