Can the USA keep printing money indefinitely? Does the debt have to be repaid?

No 

America's National Debt is approaching $30 trillion ,that's well over 100% of America's gross domestic product .When a country's debt  goes above around 75% of gross domestic product , an economy is considered to be in trouble .

At the moment , interest rates are low ,so America  can afford the interest payments . But this debt has to be  routinely rolled over. Hence ,when interest rates rise ,the debt can swallow you .

And interest rates will eventually rise .Because of America's level of debt -- future lenders are going to demand higher interest rates .

In a few years , therefore, the interest paid on America' National Debt is going to represent a very significant portion of the government (tax) income , which means that that money cannot be spent on other things .

Pretending otherwise is just sticking one's head in the sand  

Yes.

By the end of the year, your $100,000 worth of savings in your 401K will be worth $75,000.

Yes it can be repaid but usually they print money up to do that