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Well I would say a page always needs an H1. However, due to recent turn of events with Google in does not necessarily have to have your keyword in it. But it should be an H1 that is on-topic. Google is clever enough now to tell the general context of the page. As Rand said in the last whiteboard friday (HERE) there is now a lot more to on-page SEO than the old method of keyword in the url, title, description, H tags etc etc

Google has never really revealed what chrome does with the cached image. It is believed that it is stored to RAM rather than HDD. You should not be logged into Chrome at any point when checking rankings as you will automatically be using Googles personalised search.

However, if you log out, use incognito and do not actually open the sites and just do the search it will not effect the results. It is when you open sites that it will remember that as a preferred site.