Support is formed when prices stop falling, change direction, and begin to rise. Support is often referred to as a "floor" that holds up prices.
A resistance level is the point where rising prices stop, change direction, and begin to fall. It is often viewed as a "ceiling" that prevents prices from rising further.
If a price breaks support or resistance, it often continues to the next level of support or resistance. There is no guarantee that support and resistance levels will be exact; usually, they cover a narrow range of prices, so the levels may be breached or pierced but not necessarily broken. The support and resistance levels help identify possible points at which the price may change direction as a result.
This question cannot be definitively answered. In some cases, if the price can close past a support or resistance level, that level is considered broken. However, you will find that this isn't always the case.
The concept of support and resistance should be viewed as "zones" rather than concrete numbers to help you filter out false breakouts.
Finding these zones will be easier if you plot support and resistance on a line chart rather than a candlestick chart. A line chart only displays closing prices, whereas a candlestick chart also displays extreme highs and lows. In many cases, these highs and lows are just the market's knee-jerk reactions.
You don't want the market's reflexes to influence your plotting of support and resistance. Its intentional movements are the only ones you want to track.