You mean one that allows logging in and posting to Twitter aka X, without a significant fee? Not to my knowledge. Lately Elon and co. have been working to make third party clients completely impossible to develop, so it's either use the official app, use the website, or quit Twitter.
If you just want to browse Twitter, I don't know of any options for that either, but keep an eye on Nitter; currently it does not work, but they're apparently working on a way to work around Twitter's latest changes.
Depends on a few factors, AFAIK as a non-lawyer. If the license allows closed-source derivatives (i.e. is permissive rather than copyleft), then anyone can create a closed-source version with all of the contributors' changes, including the original maintainer. And anyone can choose to keep it open-source. The community contributions still to some extent belong to the contributors, though the license waives most of their rights.
Some projects are copyleft, but contributors are required to sign a license agreement (a CLA) which allows a single entity to change the license as they desire, including to closed-source - this is a good reason to avoid such projects. The contributors don't own their work in such a case, but they can still fork the old project as it was before being taken closed source.
In a copyleft (e.g. GPL) project with no CLA, it's illegal for anyone to make a closed-source version, and a major contributor could sue even the maintainer for doing so.
In all such cases, the change to a closed-source model does not erase the existence of the open-source code with community contributions. A fork is always possible.