Hello!
1. Is Arch Linux completely free? If I use Arch linux, create various programs on it, do anything in general, both commercial and non-commercial, do I have to pay anyone?
No you do not have to pay anyone, archlinux is completely free of charge. Just the use of the archlinux trademark itself comes with some rules[0].
2. What does it mean that Arch Linux has proprietary software? Does this mean I have to pay someone something?
This means that the archlinux repositories also contain software for which the source code is not publicly availiable. i.e. see the following excerpt[1] from the FAQ: "You may not want to use Arch, if you take a strong stance on using a distribution which only provides free software as defined by GNU."
3. How do I know if I'm using a free program or a proprietary one?
Check the upstream documentation of the program, from the arch side there is not much difference. You can ofc always look at the way archlinux packages the application and see whether it builds from source or not (although this is not a strong indicator).
4. Do I have to contribute to Arch Linux or is it optional?
Contributing back to arch is optional but always welcome[2][3] as archlinux is a linux distribution run by volunteers. cheers, gromit [0] https://wiki.archlinux.org/title/DeveloperWiki:TrademarkPolicy [1] https://wiki.archlinux.org/title/Frequently_asked_questions#Why_would_I_not_... [2] https://wiki.archlinux.org/title/Getting_involved [3] https://whatcanidofor.archlinux.org/