The menu text and HUD issues can be solved by having "centerMenu=1" in \Plugins\FixUp.ini. It seems that you have "centerMenu=0" in there, swissarmy, so let's fix that first and foremost and then worry about the rest.
Actually, even though RBR doesn't support that resolution (the other unsupported ones are 1280x768 and 1280x800), you should be able to use ANY resolution in window mode. The performance level may drop significantly in window mode, but still. Just make sure that FixUp.ini has "fullScreenWindow=1" and RichardBurnsRally.ini has "Fullscreen=false" in it.
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EDIT - I have to take something back now that I've tested something for the first time. I got the idea about the unsupported resolutions from here:
http://forum.rallyesim.fr/viewtopic.php?f=4&t=445. And even if that tutorial has at least one mistake on it, I have so far believed those three resolutions mentioned were unsupported in every sense of the word, mainly because with me, RBR with 1280x800 hasn't functioned ideally on my 16:10 monitor whereas 1440x900 and 1680x1050 work fine.
However, now that I tested 1280x800 on Windows desktop, I can see the similar issue as I do with RBR. The screen is not centered properly, the left side being slightly off-screen, hence the black strip on the right + the top and the bottom slightly off as well. Luckily, they're such small drawbacks that RBR's perfectly playable.
So in short, it could very well be that there are no truly unsupported resolutions in RBR (with FixUp, that is) as I first claimed, only bad monitors (or graphics cards even) that can't handle those resolutions. It's mind-boggling really, but so be it.