A higher price will likely result in more mining activity, but not more bitcoins being mined. Miners could sell a smaller portion of their mined coins to meet expenses, allowing them to keep more for themselves. Basically it's a much less liquid market, one reason why it is so much more volatile.
Those two statements don't go together. More mining activity = more costs. It will always level out, that is the beauty of mining.
Right. Difficulty and exchange rate are related, but production rate is constant until the next halving. What I'm saying is it's much easier to pump the price of BTC than gold.
The question we should be asking ourselves is whether or not to expect a pump and whether or not current price is the result of such a pump already having happened.That lack of liquidity is a huge problem. Bitcoin is basically worthless as a unit of account, even as it's utility as a store of value skyrockets because of disinflation. It's value as a medium of exchange is determined by the network capacity, which is maxing out soon unless there is an upgrade.
Unless something changes, BTC will remain a speculative commodity, not a money.