> There are things called lathes and other machine tools that can reproduce themselves.
Not unaided. Machine tools can indeed make parts for more machine tools, but they need a source of power, and a supply of stock metal shapes to do that (and eventually fresh cutting tools)
> The real question is how many of these kind of tools together with a good smelter do you need before you can be self-sufficient and keep making your own sets of tools out of raw materials?
We phrase the R&D question a little differently: What is the best starter kit, and best growth path from the kit to a fully expanded factory? We have a draft starter kit list at https://en.wikibooks.org/wiki/... , and it includes a lathe, mill, and press, which are basic machines, but there are several others in addition. The starter kit emphasizes flexibility by using attachments to do different tasks. The expanded factory can add more specialized machines as needed, since your starter machines can only do one thing at a time.
> it would be nice to get a set of these kind of tools into the hands of people in 3rd world countries
Providing starter kits for under-developed areas is one of the project goals.
> It is also something important to know about if you are planning on building a colony on Mars or the Moon,
If you can build 85-98% of your stuff from local materials, it dramatically reduces how much you have to bring from Earth. That has huge leverage on what projects are feasible. However, helping people on Earth is a more immediate and larger need. So space versions will be 3rd or 4th generation Seed Factories. The first generation design is for ordinary people right here on Earth.