1. The money stock is money plus money substitutes. The money stock declined from 1930-1933, but the amount of cash or currency did not. The decline in the money stock came from a decline in bank deposits. People generally were trying to increase their liquidity, banks included as they built up excess reserves.
2. Yes, by cutting reserve requirements in half after WWI and “managing” the money stock to be counter-cyclical, the Fed created the conditions for the massive bank failures. By 1929, Banks were highly illiquid.
3. Yes, and the moral hazard problem was made worse by Glass-Steagall in 1932 and FDIC deposit insurance in 1933.
4. There is a demand to hold money, i.e., the general medium of exchange, and not just purchasing power, which could be held in any asset. The amount of money a person will hold to satisfy his preference will depend on its purchasing power. So, you are correct that if the government inflates the money stock and lowers its purchasing power that will stimulate the demand for money and make price inflation worse. This is the process that can lead to hyperinflation.
On the Great Depression, take a look at Benjamin Anderson, Economics and the Public Welfare: