For the top bar, the easiest way to do this is to add your widget to the Top Bar widget area, but then add another widget such as a text widget before it (drag and drop to reorder widgets) but leave this first widget empty.
Now the empty first widget will be in the top left and your widget with the content will be in the top right.
The phone number cannot be replaced with something else, but you can leave the phone number empty if it’s not needed, and then check the box for the ‘Enable right of phone number’ option to add extra text in place of the WooCommerce account & cart area.