thanks a lot for your questions.
Unfortunately, such an extension of the printing feature is out of scope of the plugin. The reason is that printing is a very browser dependent feature in general, and can not be influenced easily.
Re-adding the borders to the print layout could be possible by extending a special print stylesheet, that your theme might already have. Unfortunately, I'm not into details about this, sorry.
The same holds for the styling of the Print button. While moving it below the table should be possible by just adding
Setting vertical/horizontal alignment is not possible, as far as I know, as this is a direct browser feature. But maybe it is also possible with CSS...
Adding a logo should also be possible with CSS. Basically, it would need to be hidden on the regular page, and just be shown in the printing stylesheet.