There is another path. Difficulty goes down. But most probably what’s going to happen is a mix of both price up and difficulty decrease.

Yes. But the effect is relative. BTC halving only affects new supply but there is also BTC in circulation. The total supply will not reduce by 50%, it will reduce by whatever the 50% of new daily supply was in total BTC traded that day.

But not all else is equal. At $30k btc, the halving will take $27 million in new supply off the market per day (minus whatever % miners will HODL themselves anyway). Global liquidity can add or remove billions of dollars worth of new demand within any given multi-month timeframe.

Difficulty always adjusts to the total computing power of the network.