simpleseo wrote:

Can anybody tell me if my gut fealing is right and confirm that with small text of 250 words a keyword appearance of three times is enough and with longer text of 500 words and up a keyword appearance of five times should do the trick.

There is no such evidence from search engines that we know of. Plus all websites and business niches are different. So it might look pretty silly if everybody published same-sized texts on their pages and repeated their keywords the same number of times.
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simpleseo wrote:

Also I would like to know why the different keyword density analyzers give different keyword density even with the same settings.

The inconsistencies are caused by the differences in methodologies used.