good circles and eclipse

I assume "eclipse" is a typo of ellipse? Anyway, just use the ellipse select tool (keybind: e) to make a selection in the shape that you want, then fill it in with the bucket tool (b). Hold shift while using the bucket tool to fill in the entire selection, ignoring anything that's drawn inside it. If you want to draw a ring rather than a completely filled circle, use the "border" command from the "select" dropdown menu to replace the ellipse/circle selection with its border.

how to resize selection by corner

I'm curious, what is your usecase for this? I've never had to do it myself. But if I had to, here's how I would do it: first, convert the seleciton to a path. Make sure the path is visible from the "Paths" dialog (you have to explicitly show the paths dialog using the "window > dockable dialogs" option. From then on, you can use any of the usual transform tools (perspective, resize, roate, etc) on the path. You just have to select the path icon under "Transform: " in the "tool properties" dialog to make sure you're transforming the path, not a pixel layer. Once you've transformed the path to your liking, you can turn it back to a selection, fill it with color, or stroke it with a brush by right-clicking on it in the "layers" dialog.

Also, bonus tip: never use the dropdown menus, it's a huge waste of time. Just press / to pull up for the command palette and search for the tool you need.

EDIT: I love lovingly ranting about gimp, I can do it four hours on end. I'm not some sort of gimp guru, but I know a thing or two. If anyone has any more questions, feel free to reply to this comment and I'll do my best to give advice.

Use the select tool to create an ellipse selection and go to Edit->Fill with foreground colour