If the difficulty adjusts down to make mining profitable, that's because the miner is earning more coins, but each coin is still worth less than before.
Not necessarily. While there is a positive correlation to hashrate and price, the market sets the value of the coin.
Just because miners are making more or less coins does not make them worth less or more. Miners choose when and if they release the coins to the market.
Just because miners are making more or less coins does not make them worth less or more. Miners choose when and if they release the coins to the market.