Is it possible to repay the world debt? If not, why do we care? Let me apologize if my questions sound stupid to experts. I have no training in economics. I am just curious and puzzled. I couldn't find any answer to the questions below.

As far as I have understood, broadly speaking, money is created by central banks and landed to governments with interest and creating debt.

Now, let's take a simple example. Let's imagine a world with 10 countries and 1 central bank. The central bank gives 10B (billions) to each country (100B in total) at a 1% interest rate. At the end of the year, the world owes 101B.


Where is this extra 1B coming from?
Since 1B was never created in the
first place, how can the 1B be paid back?
If it turns out that   the world cannot actually ever pay back the full debt, then why do we care? What is the use of the 1B in debt?


Of course, the countries are in business with each other. During the year some will gain money, some will lose money. The countries that managed to gain that 1% can pay back the interest, but hardly the full debt. In general, for each 1% gained by some country, others must have lost that money.

So it appears to me that with such a design 1) the debt cannot ever be paid back, 2) someone must go bankrupt in the long run and 3) the debt can only grow over time (since it cannot be fully paid back). Is that true or am I missing something?

Just to be clear, I get why we need money. I don’t get why we need debt. Wouldn’t capitalism work as well if central banks could just distribute money around as needed without asking them back? 

I don't think this question duplicates  this one. While the linked question does explain the mechanism of money and debt creation, it doesn't shine light on WHY we care about debt, nor whether  it is possible to ever pay back the world debt if it is destined to steadily increase over time.
So there are a couple of things you want to consider:

1st: It is not true that if some country gains 1% some other country must have lost that 1% of economic growth. The economy is not a zero-sum game where the gains of one person are the losses of another one. In fact, usually, it is the opposite. Think about it this way, if the US grows by a lot it also means that they will buy more things from other countries so these countries will probably also grow faster. 

2nd: Money is just the means by which we keep track of, and do transactions. At the end, what really matters is how much stuff is produced (goods or services). That is why if some country produces more things, everyone can benefit from it. 

I do understand your logic that if the Bank produces 100B of coins how can they expect to get back 101B? Once you think of it in terms of stuff, the puzzle is resolved as follows:


The bank lends you the money so you can buy and plant seeds (these are the 10B), they expect to get back some of the benefits from this productive project after you produce apples (they could directly ask to pay back in apples, but this would be impractical, that's one of the reasons we use money, so instead  they ask you for the 10.1B). Of course, if the bank does not print more money where will the .1B come from? Well, indeed the bank will never ask for 1% interest if they know there is no physical way to actually pay it back. 
What really happens is that the bank understands that if an economy is growing, she needs to constantly be printing money, so people can easily do and keep track of all the transactions they do. Therefore, when they ask for the 1% interest, first this is possible, because there is more money out there in the economy, and second, they choose how much interest to charge in order to reflect that they expect you to do something productive with the money (interest also depend, of course, on how risky is your project, and other factors).


I am over-looking the whole issue of inflation to keep things simple and explain the main logic of why banks (including the central bank) charges interests. Whenever you think about whether a debt can be paid or not; the relevant question is not if there is enough money out there to pay it. Rather the relevant question is if the money loaned is being used in a productive way so that it can later pay the interests. And if the answer is no, we care because that means that the money loaned is being wasted, instead.