The Node.js MSI installer adds C:\Program Files\nodejs\ to the system PATH via HKLM\SYSTEM\CurrentControlSet\Control\Session Manager\Environment\Path.
npm is bundled with Node.js; global npm packages installed via npm install -g go to %APPDATA%\npm\ and that directory is also added to PATH.
nvm-windows (Node Version Manager for Windows) is a popular alternative; it stores per-version Node installs in %APPDATA%\nvm\ and writes its own HKCU keys.
The MSI installer creates a Windows Installer product entry; use msiexec /x {GUID} or Add/Remove Programs for clean uninstall.
No file type associations are created by the installer; .js files are typically associated with Windows Script Host (wscript.exe) unless changed.