Pai Mei, you say <I>"The state borrows money from this corporation and has a debt to pay to it - artificial debt good only to that corporation, ..."</I>
I'd say that the money the government borrows is good for the government and for the country; with that money, the government can pay for lots of useful things. I'd prefer a balanced budget, but c'est la vie.
Then you say <i>"the people can have money with no debt - if state prints them, why borrow them ?"</I>
The economy doesn't work that way. As I've already said before, if a government could simply print money to cover their deficits, you'd get inflation. If they do not want this, they *have* to loan money from someone, be it from their own citizens or from abroad. By doing this, the total amount of money available doesn't change, hence there won't be inflation.
I expect the US government to have more control over the money supply than you think. I can only assume that, like our government, they have rules concerning the percentage banks (including the federal reserve) can lend compared to their cash. If they do not set those limits, the market will probably set them instead; after all, if a bank has too little cash to cover the loans, it runs risks. Eventually, they wouldn't be able to pay out, and they'd go bankrupt. Given the relatively low inflation and interest rates the US has had in the past, I'd say the federal reserve and banks in general are doing a good job, even if they're private entities.
IMO, there are two issues here:
1) Governments spend more than they get, leading to deficits and debt.
2) private banks can lend more money than they have in cash.
I do not believe that these issues are directly related. The economy is way more complicated than that. Getting rid of "fractional-reserve banking" (as if it's a bad thing) won't magically make debts disappear. And neither will disbanding the federal reserve.
As for the gold/silver standard:
Linking a currency to a finite resource like gold or silver means that the amount of money could never go up. This is a serious problem in today's world, with all the international trade. Given that China gets more money from the US than the US from China, for example, you could simply run out of cash. It's simply not possible these days.
One note: I just watched a bit of that documentary... I'd say it's rather one-sided. I suggest you read some books on macro economics to check the facts.