I want a close icon in the toolbar so I don’t have to keep closing and re-opening LO. I also want to be able to replace characters with special characters easily.
Please use a separate question for the second topic, but first search. You will likely find some answers. Solutions are possible with Find&Replace, with AutoCorrect or with keyboard layout.
You do not need a close icon in the toolbar. If there are more than one document open, the X in the title of the window will only close the active document, not the whole application. If only one document is open, you will get an additional x right, top in the menu bar. This x will close the document but leaves the application open, so that you get the StartCenter again.
If you nevertheless will use an icon in the toolbar, you can customize a toolbar. The needed command is .uno:CloseDoc. It is the same as item Close in the menu Format, where you can see, how the icon looks. You will find it in category Document, command Close in the Add part of the customize dialog.