LibreOffice

• You can insert new rows or columns by Highlighting a row or columns and pressing Ctrl+Shift+=
• Contrary to the advice I first read, you can move a row or column by highlighting it, holding Alt, then grabbing and dragging a cell from the row/column.

You can customise the right-click/context menus via: Tools → Customise… → Context Menus

I've found it useful to add my own styles to this list, for example (Select 'Styles' from the 'Category' drop-down to get more options).