The "order" bit is a flex-box style that only works since the parent div has a flex-box style applied.
For the borders, you need to change the border colors so that the left border is either not displayed, or matches the background-color. In the style sheet, try this:
.tc-vertical .tc-tab-buttons button.tc-tab-selected {
border-left-color:rgb(255, 255, 255)
border-right-color: rgb(204, 204, 204)
}
It should make the left border white and right border grey, matching the background color.
Another option is the adjust the border widths, and use position:relative and left:-1px to nudge the tab over, or any a few other options, but the above should work out OK for the stock TW color scheme.