Yes, the price of bitcoins depends on demand. But this will lead to the fact that the price of transactions will increase. And it's very bad. After all, one of the advantages of bitcoin was that we could pay a very small transaction.
But I believe that this problem will be solved in the future
There's no direct relation that in every increase in the price of bitcoin, the number of transactions also increases. Somebody could come in, invest 1 billion dollars, pump the price of bitcoin, but the transaction that has increased is only one. That one time when he transferred the bitcoins to his wallet. The price increase isn't necessarily caused by the demand of people. I think bitcoin is still a speculative asset and it's not built much by the number of users. It's built by the people that love playing with a market that's very volatile.
Then I do not understand what the price of bitcoin depends on? After all, many people say that the price depends on demand. And the higher the demand, the higher the price.