Does removing EXIF change my photo quality?
For JPEG, PNG, and WebP, no: the removal is a byte-surgery operation that only erases the metadata blocks and keeps the compressed pixel data exactly the same. Only formats without that support, like TIFF or BMP, go through a re-encode that can slightly alter the compression.
What exactly does GPS in EXIF reveal about a photo?
The latitude and longitude coordinates of where the camera was at the moment of the shot, and often also the exact date and time, the device model, and the settings used (aperture, ISO, exposure time). Publishing a photo without cleaning that data can reveal the photographer home address.
Why keep the ICC profile when removing metadata for privacy?
Because the ICC profile describes the image colour space (such as sRGB or Adobe RGB), it identifies no one and reveals no location; removing it only makes the photo display wrong colours in colour-managed software, with zero privacy benefit.
Does a TIFF or BMP image have its metadata removed the same way a JPEG does?
No, those formats do not have the byte-surgery support that JPEG, PNG, and WebP have, so the cleanup goes through re-exporting the image via a canvas, which decodes and re-compresses the pixels, and stops being bit-for-bit identical to the original file.