If you are dealing with SEO where you are optimizing various websites on daily basis then you can surely sense the change. Otherwise keep in touch with other webmasters you will get the info.
Despite algorithm changes- making sure your site has relevant upto date content is the only sure fire way to get good SEO results. if google sees you as a expert on a topic your site will always get good rankings.
Google Algorithm is more of a secret. It is not usually disclosed to the public to avoid abuse of the system
Is there any publicly released version of google's algorithm that non-technical people can play with?
NO. But if you can find one, I'm interested. Also on the formula of Coca-Cola. (Having stated that, there are some studies on the subject by external scholars, but they're quite technical, not complete and given the mystery that surrounds Google's algorithm you should take them with a grain of salt.)
The Google algorithm changes very often. They tweak it every day I believe. Install a stat counter and watch carefully your search engine traffic. Major algorithm changes will make it fluctuate quite a bit
You'll know when there has been an algorithm change as a whole bunch of people will start threads complain about their ranking.
I don't see Google to tell when is changing algorithms. usually people speak on forums when are modifications in traffic.
Changes in your rankings may or may not be attributable to algorithm changes. Many factors can change your rankings. In any case, all you will see is the effects of algorithm changes. Google will never release the nature of the changes, so you'll still be pretty much in the dark.
basically its minor change google will take place always but considering basic guideline for google is best.