If a random country is in debt, is printing money a good way to pay it off at the expense of the citizens?
For example, lets say you owe an entity $100. If you print an extra $100 bill you pay off your debt, but unbeknownst to the entity the $100 that they lent you is now worth less.
Would the barter system be a good way of combating this?
Not really, no. US follows this to a larger extent, since their debt keeps exacerbating by the second, and one of the many things they do to try tackle it, is print more notes. It doesn't help the situation whatsoever, rather it escalates it to a much worse scenario. The money in the market increases, yet there's no return of that money in the hands of the government. Most people don't pay the taxes, and the factor of Rich get richer, and poor get poorer comes into play. Printing more money only weakens the economy, not otherwise. Even if you try to print the equivalent amount of notes to the amount of global debt, it still won't make a difference. What will rather happen is, it will fuck up the demand and supply of the global economy, and things will go back to the same. Fair possibility is, the value of 1$ now, will be equivalent to value of 1000$ if more notes enter the economy.
How will Barter System help? It won't work even in an ideal world, let alone in a worsened imperfect world. Barter system's lack of providing the right value to the good/service was one of the main reasons it failed. The only way I see barter system coming back is through pure form of desperation, when the recession is killing the world and printed notes won't work. This was portrayed beautifully in Mr. Robot, where the whole corrupt banking system went down, and people had to resort to using crypto, and it was a catastrophe struck and no one saw it coming.