Please rephrase your question. What do you mean "its limit"? Do you mean when all Bitcoins are already mined?

The answer to that is no one knows for sure. Some say the miners will keep supporting the network and live off the transaction fees. But given that, the miners might not include your transaction if your fee given is not high enough. This will result in a competition to give higher fees maybe making transactions in BTC way higher than normal.

About your question on BTC's price increase, it might go up or down. The market decides what its price is moment by moment. But hopefully its price will be way higher than what it is right now.