Regarding 1), it's trickier than that. The issue is that there are two types of inflation, monetary inflation (more dollars floating around) and price inflation (stuff costs more money). Due to hoarding, these two types of inflation may not agree with each other. If you inflate the currency by printing money, much of it may be hoarded, since owning money is (in a deflationary environment) an investment. So the money supply increases, but consumer/investor prices continue to deflate!
Now you have large chunks of money hidden away, but prices continue to fall. This continues, until you reach a tipping point and price inflation returns. Then the hoarders spend their money, and prices inflate rapidly (price inflation catches up with money inflation). This isn't a good thing, since it's a major monetary shock, and can lead to a crisis of confidence, etc...
Probably the only way to avoid this scenario is to make sure that the newly printed money has a high velocity, but it isn't clear how to do this. The classical answer is to give it to lower income people, but it's not obvious that this will work in a deflationary environment (poor person buys TV, TV manufacturer hoards money).
You're absolutely right about the two types of inflation. In fact, any argument about inflation/deflation needs to start with throwing both words out the window. Let's use the world "dilution" to refer to increases in the money supply, and "contraction" to refer to decreases in the money supply. We'll use "price level increases" and "price level decreases" to refer to price changes, as reflected in the CPI.
If you inflate the currency by printing money, much of it may be hoarded, since owning money is (in a deflationary environment) an investment.
The government must print enough money to offset the money lost through the collapsing credit. Since the government is committing to keep the monetary base stable or increasing slightly, there is no incentive to hoard. The incentive to hoard only happens when their is a money supply contraction, not a price level fall.
A depression happens when there is a sharp contraction in the money supply due to a credit bubble collapse. Businesses that had grown addicted to credit, fail first. Consumers, expecting their debt to be diluted away, now have to save more and pay off their debts. Asset prices fall, causing a wealth effect drop in spending. The net is that fewer green bills are chasing the same number of goods, thus prices start dropping. Falling prices means less revenue for businesses. The hardest sectors hit are those that are in debt, as they borrowed assuming more money available to pay back the loans. But every sector is hit hard because of sticky wages, menu costs, etc. Businesses start freezing hiring and laying people off. The depression deepens.
The idea is that the Fed must inject money now to prevent the dominoes from falling. If the Fed prints enough money and gives it to consumers, consumers will be able to repair their balance sheets and quickly maintain or return to pre-crash spending levels. Thus all the contracts and wage agreements assuming the pre-crash money supply will be bearable, and no mass layoffs need happen. The crisis is averted
The big key is not too print too much money, or you risk triggering a hyperinflation. But by keeping a watchful eye on the hyperinflation canaries (gold, oil, and real estate) the Fed should be able to get it right.
(poor person buys TV, TV manufacturer hoards money).
That's fine - the point is to stop the TV manufacturer from having to make layoffs do to falling demand. In the real world, the manufacturer probably wouldn't hoard. Depending on their situation they might pay down debt, invest in expansion, or return dividends to shareholder.
Now you have large chunks of money hidden away, but prices continue to fall. This continues, until you reach a tipping point and price inflation returns. Then the hoarders spend their money, and prices inflate rapidly (price inflation catches up with money inflation). This isn't a good thing, since it's a major monetary shock, and can lead to a crisis of confidence, etc...
Probably the only way to avoid this scenario is to make sure that the newly printed money has a high velocity, but it isn't clear how to do this. The classical answer is to give it to lower income people, but it's not obvious that this will work in a deflationary environment (poor person buys TV, TV manufacturer hoards money).