"Geotagging photos" means that you attach latitude and longitude coordinates to a JPG poto file. This information is saved in the metadata of the JPG file and is not visible on the photo.

Yes and no! For JPG files the way to attach geotags is standardized and that's why it's useful and can be processed by many other websites and tools. Other image file types do not not officially support geotagging. That's why this website only supports JPG files.

No, that's not possible. The geotags in JPG files can be changed afterwards (for example with GeoImgr). That's why it's not possible to know where a photo has been taken.

See Wikipedia: https://en.wikipedia.org/wiki/Geotagging

GPS Latitude                    : 57 deg 38' 56.83" N
GPS Longitude                   : 10 deg 24' 26.79" E
GPS Position                    : 57 deg 38' 56.83" N, 10 deg 24' 26.79" E

The easiest way is using your Android or iOS smartphone. You just have to activate the "save location in photo" option. New cameras with GPS sensores also support geotagging. For cameras that do not have GPS sensors you can use geo trackers (see question below).

In this case you can use a software (e.g. geoimgr.com) to add geotags manually to your photo files. You can also use a GPS Logger device (see below).

You can use a GPS logger/tracker device to log your location in certain time intervals (seconds or minutes) and afterwards match the photos with the corresponding location using the timestamps.

If you save geotags in photos and you share the photo files then other people could see where the photos has been taken etc. However if you send the photos using instant messenger apps from your smartphone (e.g. WhatsApp) as images then the app will usually send a modified image file that does not contain the geotags.