Write new text onto a PDF page, choosing the font, size, colour and position. This adds a fresh text layer over the existing content, which is what you want for filling in a printed form, adding a note, or labelling a diagram. It does not alter the words already in the document - editing those is a different job.
Not really. This adds text on top, so the original word stays underneath and would show through. The PDF Text Editor changes the text already in the document, which is what a correction needs.
Yes. It is added as real text, so it can be selected, copied and found with a search, unlike text drawn into an image.
For a label repeated across the whole document, Add Watermark or Add Stamp is designed for it, and Add Page Numbers handles running numbers with correct placement.
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.