I clean my varnish brush thoroughly after each use. I dip and rinse the brush in 4 separate cups of solvent/thinner to remove as much varnish from the brush as possible. Then I dab the brush with paper towels to draw out as much solvent as I can. I finish up by washing it with soap and water. BTW, the Master’s Brush cleaner is great for this. I actually have a tutorial of this procedure on my website http://www.nitpickyartist.com/varnishing-a-painting.html . Its located at the bottom of the page.

You should be okay varnishing the white areas of the painting. Most synthetic varnishes are as clear as water and have UV protection in them, so yellowing will not be an issue. And even if you did use a damar varnish which naturally has a pale yellow tint, the coat of varnish you lay down will be thin enough to where it wont be noticeable. However, damar does yellow with age, so beware

Anyone varnish over a painting that has a lot of white canvas exposed?

No. I never leave canvas exposed and then varnish over it. I have at least one coat of paint on it (a gessoed surface, of course).

Yes, that’s actually what I have, too. I have gesso over the canvas. I guess what I want to know is what people think about the white from the gesso – does the varnish affect the strength of the white?

Nope. Should remain the same. Just a change in surface sheen.