Then that cost will decide its value. For PoS coins' value to rise, the mining cost must go up, and eventually it will be as energy hugry as PoW coin
If people can both mine coins and buy coins, they will always select the cheapest method to get coins (provided coins have some use). So eventually the mining will become so energy consuming that it costs almost the same as coin's market price, which makes PoS coin the same as PoW coin. Actually I don't think you can design a scheme to overcome this basic market behavior, unless you can make a law to force people to use PoS coins
Well sort of. A coin's value is determined by supply and demand, not the mining costs;
it is the mining costs that are determined by the value of the new coins being issued..
PoS coins like NXT have essentially no mining (minting) costs because they issue no new coins.