Lot of questions...
How much watercolour painting experience do you have? Learning good brush control helps. Beading up sounds like you have either have too much solution on your brush or your paper is being really weird and resistant to the liquid all together.
Changing paper can help with the blues. I double coat with a hake brush for mine. BFK Rives works okay but it's a bit soft & spongey as far as papers go and if you're rough brushing it, it can look a bit fuzzy. Look for an unbuffered paper, they're usually cheap. Cyanotypes prefer acidic enviroments and don't like buffered and acid-free papers.
As far as clarity of image, what are you using for your contact printing frame?