No, I was referring to the textbook definition of supply, which is the function of units offered at a given price. As the price goes up more units are offered.
No, that is quantity supplied. Supply = total BTC available. Money supply (M0) is ~6.7million currently. At any given price there is a different amount of quantity demanded and quantity supplied. At $0.01 quantity demanded is very high and at $10,000 per BTC quantity supplied would be very high. When talking about 'Supply' we're not talking at a specified price, we're talking about total available to be supplied in the market.
People also keep thinking that the mined coins are the only supply and that they all go onto an exchange immediately and that they sell regardless of the price. All of these things aren't true. Before Mt. Gox went down, the daily volume was 8 times the mining rate, we all know that miners hoard their btc, and if the market rate goes down, a lot less people would sell. Similarly, if the cost to mine goes up, then the supply curve will move. This is very basic economics.
No, if the cost of mining goes up the supply curve will not move. You are confusing terms and concepts. If people suddenly start paying $100 to mine 1BTC that won't suddenly move the market to meet that price - it just makes those people incredibly stupid. A shift of the supply curve to increase price would mean that supply would be decrease (cost of mining does not change the amount of bitcoins entering the market!).
We all know that miners hoard their btc? How do we know that? Miners aren't some weird exception to the market. Every bitcoin owner/buyer has preferences and acts somewhat rationally (to a varying degree). Everyone wants to buy low and sell high. Nothing about the increased cost of mining would cause people to suddenly be willing the pay a greater amount for the same amount of BTC (a shift in the demand curve).