I don't understand what will happen in the next halving time. Will it be harder to mine, which means less bitcoins produced and that will drive up the btc price?
Yup, this should be it, price going double..
Basically, no. Price comes first from the minds of the individuals (us), mining cost will fall in line. When block reward goes to 12.5 BTC/block, the cost of mining a block will eventually also be 12.5 BTC.