But how to adjust it using Qt Libs?

Either version of QWidget::setTabOrder()

is it possible to move between buttons and lineEdit using arrows?

In the case at hand:
Arrows/No.
Tabs/Yes.

Arrows will navigate between widgets as long as they don't have input focus. Once the cursor is stuck in a line edit, only tab will move it. You can subclass QLineEditto implement arrow based focus changes.

Don't forget: the only thing saved from Designer is the .ui file. So anything/everything you do there must be in that file. And then you run uic to read that and produce file named ui_....h. (This is put in the build output directory, not the source directory. If you are Python it's a .py file.) And these are included/imported into your code file, you can examine them in editor and see what code it produces for your .ui settings. That can be really useful for understanding how to do things in code which you did in Designer. The tab stuff would be in this.

I don't know about your arrow keys. You would normally use Tab or Shift+Tab. In any case, the interface for moving around should follow the desktop window manager's way of doing things (which Qt will do), rather than inventing your own non-standard way, which would just confuse users.