Well, if someone is looking to spend in BTC and they choose to acquire it via mining, then that one less block (or part of the block) in the supply side of the market for currency exchange, which effectively makes the price go up (or not go down as much) all else equal. If they instead let someone else mine it and buy that 50BTC, theoretically the price should go up about the same (or not go down about the same), assuming everyone's preferences for BTC and USD are the same in both situations. Again, it does not affect price.
It's not true that btc supply is limited. If we stuck to 6 block an hour then there wouldn't be difficulty increases. But actually, that doesn't matter even assuming supply of btc is fixed and the demand of btc is fixed. The actions of the person determine the equilibrium
Again, the three are related through the equilibrium. Assume someone wants to transact in bitcoin but they have none. If it is cheaper to mine than buy (e.g btc at $200), they will invest in mining but this will push the difficulty up. Everyone acting together pushes the difficulty up until mining is at parody with buying.
If it is cheaper to buy than mine (e.g. btc at $5), then the person will have to buy bitcoins which drives the price up.
Price is the intersection of quantity demanded and quantity supplied. In your situation that quantity does not change. If price to mine jumped up to 100x the price it would not change the quantity demanded or supplied for BTC, just shifts where people spend their money to acquire it (assuming difficulty adjusts fast enough, which is the only lagging factor than can affect price because it means more (or less) than 6 blocks an hour on average are being created)
Something to note is that there is a bit of a difference in demand in these two scenarios. People don't have a demand for btc, they have a demand for the transaction. Let's say they want to use btc to buy a spot troy oz of silver ($36.25). In the first case they need .18 btc, in the second case they need 7.25 btc. Even though the real demand is the same, the nominal demand for btc is higher when the price is lower (this is an econ forum, I hope that is obvious).
It seems like you are treating btc like a thing and not a currency. You can't eat, sleep in, or fuck a btc. You use btc to eat, sleep, and fuck.