Re touch up:
White is one of the most difficult colors to fully match and touch-up. A normal human eye is quite good at discerning subtle variations in the white: flat/gloss, faded/bright, minty tints, cream/off-white tones, etc. It's certainly possible to get a good match, but you're going to be working hard to manually mix your paints until you get a true match. If you're lucky, an auto paint shop or paint store can match using a computer, but even those can only get so close. And any paint you mix may match one part of the bike, but not another because of irregular fading over the years.
This is not to discourage you, but it is to say that you need to be ready to make good touch-up on an old, white bike a project of sorts. With a large area of old, white paint like that, it's going to be hard (or very lucky) to pull a bottle of flat or semi-gloss (or whatever) white off the shelf and have a spot-on match.