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No, I'm using words in standard meanings: "anchoring" means limited to the vicinity of a particular place or value, and "capped" means can go down but cannot go up above a certain limit.
Yes, under the assumption of many separate agents. However people can cooperate if there are sufficiently large incentives for that and there's no anti-trust authority to stop them in the Bitcoin world. One mining pool already got over 50% of world capacity at one point -- it quickly backed down for obvious reasons, but my first guess at an attractor point (equilibrium in econospeak) would be a duopoly where two mining pools control most of mining and they may or may not collude.
How are you suggesting they manipulate prices? While there are a number of security flaws, none of them allow counterfeiting. You can't increase the supply beyond what it should be no matter what you do. You can destroy bitcoins by sending them to invalid accounts and cause deflation that way, although I have no idea why you'd want to. You could get over 50% of mining capacity and frequently use it for the 51% attack, causing people to lose trust in bitcoins and making the price fall, but again, it's not going to help you.