To analyze the properties you mentioned from a user agent string, you can use a parser library or tool. Here are some examples:

Device model: You can use a user agent parser like DeviceDetector, which can detect the device model from the user agent string.

Rendering engine name and version: The rendering engine is usually mentioned in the user agent string. For example, if the user agent string contains "Gecko", then the browser is likely using the Gecko rendering engine. Similarly, "Trident" refers to the Internet Explorer rendering engine, "Blink" refers to the Chrome and Opera rendering engine, and "WebKit" refers to the Safari rendering engine. You can also use a parser library like UAParser.js, which can extract the rendering engine name and version from the user agent string.

Language preference: The user's preferred language can be detected from the "Accept-Language" header sent by the browser. You can use a library like accept-language-parser to parse this header and get the language preferences.

Screen resolution and color depth: The screen resolution and color depth can be determined using JavaScript. You can use the screen object to get the screen width, height, and color depth.

Cookies supported: The user agent string does not contain information about whether cookies are supported or not. However, you can use JavaScript to check if cookies are enabled by trying to set a cookie and then reading it back.

Referrer website: The referrer website can be obtained from the "Referer" header sent by the browser. You can use a server-side language like PHP to access this header and get the referrer website. However, note that some browsers may not send the "Referer" header for privacy reasons.
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