Reduce the file size of a PDF. You can pick a compression level, or give a size you need to come in under and let the tool work towards it. Most of the saving comes from re-encoding images, which is why a scanned document typically shrinks enormously while a text-only PDF barely moves - there is very little to compress in a page that is already just text and fonts.
It depends almost entirely on what is in it. Scans and image-heavy documents often drop by 70 to 90 per cent; a text-only PDF may barely change, because its size is fonts and text rather than image data.
At higher compression levels, yes - images are re-encoded more aggressively and the loss is permanent. Start with a moderate level and increase it only if you need to.
That usually means it was already efficiently encoded, or it is text rather than images. Converting to greyscale helps if it is a colour scan; beyond that there may be nothing left to recover.
No, the text layer is preserved, so a document that was searchable stays searchable.
Files are uploaded over an encrypted connection and processed on CoonTool's own server, not in your browser. The working copy is deleted automatically once the job is done, and in any case within 24 hours. Nothing is stored permanently and no account is required.