Recording your screen usually means installing something, and the free ones stamp a logo across the result or stop after five minutes. This records the screen, the camera, or the screen with the camera tucked into the corner, mixes your microphone with the sound coming out of the tab, and hands you the file. It runs on the browser's own recording machinery, so there is nothing to install, no length limit, no watermark, and the video is never uploaded.
Neither. There is no upload step to charge for and no branding to add, so the only real limit is disk space and the memory the tab has to hold the recording in. Long sessions are fine; a recording measured in hours is where you would start to feel it.
Almost always because the system-audio tick box in the browser's share dialog was left off. That dialog belongs to the browser rather than to this page, so the toggle here cannot force it. Chrome offers it when you share a tab and, on Windows, when you share the whole screen; on macOS the whole-screen option does not include system sound at all. If you only wanted your voice, check the microphone permission instead.
WebM in Chrome, Edge and Firefox, which is what those browsers record natively and what every video editor and upload form now accepts. Safari records MP4 instead, and the page picks whichever the browser actually supports rather than asking for one it does not. Converting WebM to MP4 afterwards is a re-encode and is best done in a video tool.
Yes. A video file can only carry one picture, so the screen and the camera are drawn together onto a canvas while you record and that composite is what gets saved. You cannot separate them afterwards, which is the trade for not needing an editor.
No. Screen capture from a web page is not available in Safari on iOS, and the page says so rather than presenting a button that does nothing. iOS has a built-in screen recorder in Control Centre, which is the right tool there. On a desktop, Chrome, Edge and Firefox all work.