Answers to your questions about inflation.

Monetary inflation is an increase in a country's money supply, influenced by the interest rates and other monetary policies of central banks. When a central bank prints money for the purpose of monetizing a country's deficit spending and debt they are creating monetary inflation.
Price inflation can be in the form of consumer price inflation or asset price inflation. Consumer price inflation is measured by a country's consumer price index (CPI). The year-over-year percentage increase in CPI is equal a country's official price inflation rate. Consumer price inflation is a symptom of monetary inflation but also influenced by the velocity of money. Asset price inflation is an increase in the value of assets like stocks and Real Estate as a result of monetary inflation and not real fundamentals.
Velocity of Money is usually used to refer to the ratio of a country's nominal gross domestic product (GDP)/M2 Money Supply.
The M1 Money Supply of a country includes their total supply of cash and checking deposits. The M2 Money Supply includes the M1 Money Supply plus savings deposits, money market mutual funds, and other time deposits.
A country's monetary base is directly influenced by their central bank's open market operations and monetary policy. It includes currency in circulation plus reserve balances held by banks. It is considered to be "high-powered" money due to its ability to multiply in a fractional reserve banking system.
Since 1971, the U.S. dollar has been a fiat currency that is backed by nothing other than faith and confidence that it will always retain its purchasing power. Nothing restrains central banks from printing them out of thin air. All international currencies of all countries today are fiat currencies.
The U.S. had a gold standard from 1873 through 1933 that allowed people to exchange $20.67 for one oz of gold. In 1934, the U.S. dollar was devalued so that $35 was needed to trade for one oz of gold. From 1934 through 1971 only international countries were able to exchange their U.S. dollar accounts for gold. In 1971, the U.S. completely eliminated its gold standard and the U.S. dollar became a fiat currency.