Shapeshifter - 80 grit in a random orbital sander (ROS) is way too aggressive in my opinion. To get things smooth you will now need to go to 150 grit then to 220 grit if you want smooooth. Some go higher, some stop at 150 grit. Oak veneer, as you probably know, is very thin. Its easy, if you are too aggressive in sanding, to blow through it.
To answer your question. ROS doesn't really need to go with the grain, I do when I move it around on the surface.
As to the different colors of wood. This is common on some types of store bought pieces. The manufacturer uses what ever wood they can get and then uses stuff called toner to even out the color. Toner is in a spray and is part of a factory applied finish. Some stains may work to even out the color as well. The minwax stuff would be your last choice for this. You are more likely looking for a gel stain or dye to even the color out. All of these are going to darken and change the color some. (Necessary to even out color).
Personally I like to use toner. I do not have pro spray equipment but for small projects you can buy it in a spray can. behlens is one brand. Woodworkers supply has it. Its also called Lacquer toner. Just spray a color you like then I just top coat it with the same brand clear lacquer, also in spray cans.
When I use the spray lacquer I sand to 220, apply toner if desired, let dry, lightly, by hand sand with 320 or 0000 steel wool. Spray another coat of clear lacquer, 0000 steel wool and a final clear lacquer coat and call it done. Its a very durable finish and the stuff drys very quickly (minutes). Its certainly not a traditional finish, nor is it common, It is tough and its easy.
See
http://www.woodcraft.com/family.aspx?familyid=7235