I sold 2/3 of my bitcoins (after 1 month mining), I'm debating whether I should continue to sell the rest.

The basic argument here I see is bitcoin is better than USD because its supply is limited and won't expand. In other words, a lot of people hold bitcoins to hedge against USD inflation (at least that's one of the many reasons).

So my question is if bitcoin/USD exchange rate continues to fall or even remaining constant, does it mean bitcoin is also being inflated (even without the increase of its total quantity)?

I can understand how gold or even real estate can hedge against inflation because they have real value. For bitcoin, it's just another currency whose value is yet to be determined...