Sorry for the late reply. Christmas season and all. Merry Christmas everyone 
So interesting and diverse responses here, which is great. My thoughts on the points bought up:
POINT 1:
So from a game theoretic perspective of the miner, we can consider that they would like to increase the profit of their operation. The profit they make comes from fees of transactions included in the block and the block reward which is 6.25BTC. So as the price goes up, they can sell those BTC for cash to pay bills and re-invest in their operation. This chart shows the block reward in BTC and in USD dollar for a visual on how price effects a miners profit https://bitcoinvisuals.com/chain-block-reward.
Game theoretically, a miner wants to increase their chance of earning that block reward and fees by being the first to produce the block. This can be achieved by placing more hashing power on the network. So as the profit of a miner increases, they would put more hashing power the network to increase their chance of earning the next block's reward and fees. Of course they only do this to the point in which it is feasible, as hashing power uses electricity which costs money, contributing to the overheads of their business. Over time, as the block reward depletes via halvings, the significant source of income for a miner will be the transaction fees. At which point, people transacting on the BTC blockchain will determine how much hashing power exists on the network which provides security to the ledger, through their fees.
Here is the connection: as the price increases, miners put more hashing power on the network, the difficulty rises, which increases the computational power required to mine a block. computational power consumes electrical power. QED BTC price is connected to energy consumption. As this scales, it becomes a factor of consideration in environmentally sustainable operation.
So interesting and diverse responses here, which is great. My thoughts on the points bought up:
POINT 1:
How do you plan to connect the price of bitcoin with the energy consumption or sustainability?
So from a game theoretic perspective of the miner, we can consider that they would like to increase the profit of their operation. The profit they make comes from fees of transactions included in the block and the block reward which is 6.25BTC. So as the price goes up, they can sell those BTC for cash to pay bills and re-invest in their operation. This chart shows the block reward in BTC and in USD dollar for a visual on how price effects a miners profit https://bitcoinvisuals.com/chain-block-reward.
Game theoretically, a miner wants to increase their chance of earning that block reward and fees by being the first to produce the block. This can be achieved by placing more hashing power on the network. So as the profit of a miner increases, they would put more hashing power the network to increase their chance of earning the next block's reward and fees. Of course they only do this to the point in which it is feasible, as hashing power uses electricity which costs money, contributing to the overheads of their business. Over time, as the block reward depletes via halvings, the significant source of income for a miner will be the transaction fees. At which point, people transacting on the BTC blockchain will determine how much hashing power exists on the network which provides security to the ledger, through their fees.
Here is the connection: as the price increases, miners put more hashing power on the network, the difficulty rises, which increases the computational power required to mine a block. computational power consumes electrical power. QED BTC price is connected to energy consumption. As this scales, it becomes a factor of consideration in environmentally sustainable operation.