Drag across the part you want to keep. The rectangle can be free or held to a shape, the exact pixels it covers are shown as you move it, and the cut is made on this device.
Measured against your picture
Nothing cropped yet
Tap “Draw the area to keep” first, then drag across the picture; tap it again when you are done and the page scrolls normally. That extra tap exists because iOS treats a drag on a picture as a scroll and takes the gesture back mid-drag — measured on an iPhone, a drag on an always-on surface produced a cancelled gesture and no rectangle at all. Making drawing a mode is what makes it work with a thumb.
The pixels you keep are the pixels you had, at the same size — nothing is scaled up or down. A JPEG is written again by your browser's encoder at high quality, which is a second lossy pass and is very nearly invisible; a PNG is lossless and loses nothing at all. What does change is the file size, because there is less picture in it.
Yes. Choose the shape before you draw and the rectangle is held to it however you drag, which is the reliable way to get a square profile picture or a banner that fits. Free is the default, because most crops are not a shape — they are a thing in a photograph.
No, and deliberately. The rectangle is drawn on one picture; applying it to a second one of a different size or shape would cut a different part of it, silently. One picture at a time is the only version of this tool that cannot get somebody's head cut off.
No. The camera model, the exposure, the timestamp, any editing history and any GPS position are cut out of the finished file, and the finished file is then measured: the result panel reports how many bytes of that data were in your picture and how many are in the copy you take away. The colour profile is kept, because dropping that would change how the picture looks.