In response to your edit, no. There is no set cost to mine a bitcoin. Energy is expended in trying to solve the problems the generate bitcoins. Once bitcoins run out, this is still true as instead of directly creating new bitcoins, miners will still be rewarded with the transaction fees connected to whatever block they main.

The difficulty of solving a problem to generate coins is dynamically and automatically adjusted such that it takes about 10 minutes. What this means is that if you had a total of 800 nuclear reactors dedicated to exclusively powering ASIC systems to mine Bitcoins it'd take, on average, just as long as it would if your total electricity consumption was the equivalent of one guy running a low power laptop using a hand crank or bike generator.

So all the electricity consumption represents is demand. As demand increases for bitcoin, so does this price. When the price goes up this means you can afford to pay more for electricity and still show a profit. When demand goes down for bitcoin you need to pay less and less for electricity to maintain profitability.

What will happen when no new coins are being generated is that the reward for each block mined will decrease. This will mean you receive less money for mining a block and thus can not afford to pay as much for energy and remain profitable. The net effect being that we'll see a decline in energy usage as miners running on thinner margins are pushed out of profitability.

The dynamic balancing is actually quite a clever design.

Minting of new coins is an exponential decay (hence the mining metaphor, gold becomes rarer to find as mining continues). There's also transaction fees which are based on supply/demand for blockchain operations.