Most questions have a one-line answer. If yours is not here, write and you will get a reply.
The button lives in the player controls, at the right end, just before the settings gear. It is not in the toolbar. If the tab with the video was open before you installed the extension, reload that tab once.
Straight to your downloads folder, named after the video with the timestamp in brackets, for example Lecture 04 [12-04].png. If your browser is set to ask where to save every file, it will ask.
It should not be. The frame is captured at the resolution of the video, not the size of your player, so a 4K video gives a 4K image even in a small window. If you are getting the size of the window instead, you captured with the system screenshot tool rather than the camera button.
That happens with protected players, which block the picture at the driver level. Ordinary YouTube videos are not protected and capture normally. If a specific video gives you a black frame, send the link.
Set the frame rate to match the video. Open the panel from the extension icon and choose 24, 25, 30, 50 or 60. A 60 fps video stepped at 30 lands on every other frame.
Both are in the panel behind the extension icon in the toolbar. Chrome hides new extensions under the puzzle piece, so pin it once and the icon stays in view.
Yes to all three. The camera stays in the player controls in every mode, and shorts capture in their own vertical aspect ratio.
Write to shardintoy@gmail.com. Include the video link and what you expected to happen — that is usually enough to reproduce it.