Adding shadows isn't too hard to do to all the text in the game, but it's more complicated to do it in just one specific place. Maybe check out
this tutorial, but it's a fairly advanced tutorial that teaches you
how to script it instead of just giving you the code. I don't really have time to write a simpler one, sorry! (Summary in case you're capable of scripting: the simple method is to overload the draw_text method to always run a second draw_text, with the same text, in black, one pixel down and one pixel to the right of the original text.)
Fixing the Spirit text is much easier. You just have to change one number in one line of the default scripts. Open up the script editor and click on the Window_Base script on the left side. Go down to line 250, which should be
self.contents.draw_text(x, y, 32, 32, $data_system.words.sp) and change that first 32 to a 64. Save it and you're done.
Regarding the backgrounds, I would recommend stretching them proportionally and then cropping them to fit the area.