Yes, uv can install Python: https://docs.astral.sh/uv/guides/install-python/

There are a bunch of environment variables for controlling where it puts things, here's one that looks relevant: https://docs.astral.sh/uv/configuration/environment/#uv_pyth...

Yes. Uv can install specific Python versions from python build standalone (they have taken over maintenance for it https://astral.sh/blog/python-build-standalone ) instead of from python.org because python doesn't release relocatable binaries (and doesn't release binaries for Linux I think). It works well but does have a few minor https://gregoryszorc.com/docs/python-build-standalone/main/q...

Im fairly certain the answer to this is “yes”. Probably need to futz with env cars to get all the caches etc into /tmp though. It needs to put Python _somewhere_

Yes - in fact I recently uninstalled pyenv and poetry, switched to uv, used it to install python and poetry (for work projects)