Both Bitcoin as well as Bitcoin Cash use a proof-of-work algorithm to timestamp every new block. The proof of work algorithm used is the same in both cases. It can be described as a partial inversion of a hash function. Additionally, both Bitcoin and Bitcoin Cash target a new block to be generated every ten minutes on average. The time needed to calculate a new block is influenced by a parameter called the mining difficulty. If the total amount of mining power increases, an increase of the mining difficulty can keep the block time roughly constant. Vice versa, if the mining power decreases, a decrease of the mining difficulty can keep the block time roughly constant.
When people talk about the price of Bitcoin, they are referring to the current price at which Bitcoin is changing hands. Since Bitcoin is a purely speculative asset, this price is determined by how little sellers are willing to charge and how much buyers are willing to pay. Even then, the price of Bitcoin can vary across exchanges like Coinbase and Binance or currencies because of market inefficiencies
To keep the block generation time equal to ten minutes on average, both Bitcoin and Bitcoin Cash use an algorithm adjusting the mining difficulty parameter. This algorithm is called the difficulty adjustment algorithm (DAA). Originally, both Bitcoin and Bitcoin Cash used the same difficulty adjustment algorithm, adjusting the mining difficulty parameter every 2016 blocks. Since 1 August 2017, Bitcoin Cash also used an addition to the DAA, called an Emergency Difficulty Adjustment (EDA) algorithm. EDA was used alongside the original DAA and it was designed to decrease the mining difficulty of Bitcoin Cash by 20%, if the time difference between 6 successive blocks was greater than 12 hours.
With the largest variety of markets and the biggest value - having reached a peak of 18 billion USD - Bitcoin is here to stay. As with any new invention, there can be improvements or flaws in the initial model however the community and a team of dedicated developers are pushing to overcome any obstacle they come across. It is also the most traded cryptocurrency and one of the main entry points for all the other cryptocurrencies. The price is as unstable as always and it can go up or down by 10%-20% in a single day.