Verdict: Yes
Yes. Unity make a Linux version of the Unity Hub and the editor, and Unity's own documentation says the Hub installs on Windows, macOS or Linux.
Unity run their own software repository for Linux, so once it is set up the Hub installs and updates like any other program on your system. Through the Hub you then install the editor versions you need, the same way you did on Windows.
Ubuntu is the distribution Unity officially support. They also give instructions for Red Hat Enterprise Linux, CentOS and Fedora, while saying those are not officially supported and come with no guarantee. If you want the smoothest run, use Ubuntu or something built on it.
Your projects open. A Unity project is a folder, and it moves between systems as it always has, along with your account, licence and Asset Store purchases.
Two honest limits. Setting up the Unity repository is a job for the terminal, so it is not a double-click install. And building a game for some target platforms still needs the right tools installed, which is the same situation as on Windows.
Free open source game engine with no licence fees. A genuinely different editor and scripting setup, so existing Unity projects do not carry over.
Your files: Unity projects cannot be opened. Art, audio and 3D models can be reimported.
For the modelling and animation side rather than the game itself. Free, and already the standard 3D tool on Linux.
Your files: Opens .blend files and the usual 3D exchange formats.
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