no, it is not true. AdSense displays ads based on how well a specific ad is doing and how relevant it is to your site. it may not always be the highest paying.
No because if it was true you didn't get 3 cents per click. It's not a simple system, there are a lot of other things that determine the which ads to display.
keywords in the ad, relevancy to the content, whether or not there are other high-performing ads already in rotation for that themed-site, items like that.
I guarantee it does. Most publishers hurt themselves by overplacing ads. When I push my ad units to the maximum units with the maximum ads, my CTR was high but CPC was terrible. On one not very well paying site I dropped my ad units to 1 small 234x60 and my CPC skyrocketed. One ad displayed with the maximum payout. Sure, fewer people clicked it, but the payout was the best. I've cut back on ads on other sites and the CPCs went up immediately. Yesterday I changed my most popular site (cutting ads in half the number) and I woke up to 4x the usual morning income.