Letting an app crop your photo automatically usually cuts off the wrong thing. Cropping it yourself takes ten seconds and keeps what matters.
Cropping decides what is in the picture. Resizing decides how many pixels it has. Doing them in that order means you never stretch anything.
For a profile picture, leave a little space around a face rather than filling the frame. Most platforms display it inside a circle and will clip the edges.
Cropping never costs quality. You are keeping fewer of the original pixels, not rebuilding them.
Choose the square shape and drag the box over the part of the picture you want. The box keeps its proportions as you resize it, and its pixel size is shown, so you can see how much of the picture you are keeping. Move it until the subject sits where you want it.
For a face, keep the eyes about a third of the way down. If you will post the result on a site that shows a smaller version, save a large crop and let the site shrink it, or resize afterwards with Resize image to an exact figure such as 1080 by 1080.
Crop square here, then resize to whatever the platform asks for, commonly 400 by 400 or larger.
The same tool rotates and flips as well as crops.
No.
Yes. Drag the box to move it, or drag a corner to change its size. It keeps its square shape the whole time.