You can run them locally, yes. There are models that can even run on phones, but usecase is limited. But it can only be considered ethical, if the training data used is listed or ethically sourced IMO.
AI bros on Lemmy will disagree with me, but most open weight models are still trained unethically i.e, theft. Most proponents of LLMs (who I talked to on bsky), who say local models are ethical, don't fucking use it. They're larping on socials about how awesome it is, but none of the ones I talked to are using it in their projects. They mess around, realise it is not as good as the "unethical" options, go right back to Claude
Open weight models Qwen, deepseek, mistral, and the Ollama stuff etc are unethical in normal people's eyes, but "ethical" enough for AI bros.
From what I searched, there are very few that can be considered ethical - Olmo, Apertus, Starcoder(?). But idk anyone who uses these. My friend at IBM said they used Apertus, but it was nowhere near good as ChatGPT, so they no longer use Apertus now. And these models require minimum 6-8 GB VRAM for their lowest parameter model iirc.
Even the open-weight model bros are lobbying to redefine what 'open-source AI' means. That should give you a fair idea about people behind open-weight as well