Hello, does someone know if there is some relation between number of visitors (some of them probably have Google toolbar and are tracked by Google) and PR of my site or SERPS?
If you're asking if the number of visitors increases your PR or serps, then no. If you're asking if having high PR or serps necessarily means a lot of visitors, again - no. There is absolutely no way of making an evaluation of visitors based on PR or serps. For example, an extremely niche academic site could have a high PageRank based on longevity, and on having lots of high quality back links from, for example, University and Governement sites, but have very few visitors precisely because it's so specialised and only a handful of post-grad students have an interest in it. Likewise, a site could be at the top of serps for a keyword that is rarely searched for - again, very few visitors.