In 50 years or more from now, what will happen with bitcoins when all of them are issued? Will mining stop and will there only be a limited amount of bitcoins in circulation?
Yes there will be a point from when on there are no new bitcoins. This is a point which makes bitcoin interesting for people because there cannot be inflation by creating new money. Currencies which are controlled by govnernment can easily add new money and cause inflation.
Regarding the mining I am not sure but it should still exist because it is needed to create new blocks in which transactions are stored, therefore, mining is always needed, but they could lower the difficulty. Even though this is speculation.
Once all the bitcoins have been mined, or even close to it, the situation will become more interesting. The more people continue to adopt it the price will continue to rise. Hopefully bitcoin, or some other crypto currency will become accepted world-wide. Since rising population means more and more people adopting it, the amount 1 bitcoin is worth will continue to rise, leaving more people using fractions of bit coins that will be worth what one bit coin was worth a few years before.
What this means:
1.) Poor people, who are able to save very little will find themselves much wealthier as populations increase just by saving a little (poverty will not be permanent for anyone). Instead of there being inflation, rising population will cause deflation. Anyone who saves money, including those who are already wealthy, will grow wealthier with each person born.
2.) Research in maintaining the health and increasing the lifespan of a population will become more important. It would be in the "Power Elite's" own selfish interested to keep individuals alive and healthy for as long as possible to ensure the highest possible number of transactions to maintain and increase the amount their own bitcoins value. There are roughly 0.003 bitcoins for every person on the planet. If this form of money or payment were to be accepted by all, this number would decrease with each person, causing it to become more scarce, leading to higher value.
3.) War would become unprofitable since the value of bitcoin depends on the number of people who possess it. If a country goes to war with another and decimates a population, those leading the charge would find their wallets smaller when the war was over. Fewer people=Fewer people with wallets=Lower value... End of war?
4.) The way people invest would change: more people would invest in live saving, prolonging, technology to increase value of the cryptocurrancy instead of war.
5.) New Language would develop; we are seeing this already with phrases like "mBTC" or "millibitcoin". If it is successful we could hear phrases like "nano-bit" to explain the price of a product since the price of one bitcoin would be such a high value, it would be as common as someone claiming to have a million dollar bill.
6.) hundreds of years from now people will look back at our paper currency system and think one of two things. 1.) They will see how the world descended into wars as the nations of the world started to go bankrupt, like hungry animals backed into a corner or 2.) our paper currency will seem as strange to them as Native Americans trading beads. And the pioneers of cryptocurrancy will look like the settlers of that new world, trading those beads for their land, leading to a revolution and changing the world... minus the genocide ;)