Price action is exactly what it says it is. It's the way price acts or moves, and it is studied by plotting the price using charts. This movement of price is the basis of technical analysis as traders study charts to identify patterns that they beleive can help them predict the price movement.

Trades use various kind of charts, e.g. candlesticks, renko, bars, heikin ashi among others to help them derive meanings from price movement, e.g. bullish hammer pattern formation after falling prices in a stock may be considered as a signal of trend reversal. Apart from the patterns, traders use supports and resistance, trendlines, trading volumes and other information as they see fit to make sense of price action.

There are plenty. Every broker has either their own charting kit of integration with another popular charting software. Zerodha has kite (chartiq) for charting and also have an integration with TradingView. 

My favorite is TradingView. It has a free plan and NSE/BSE data is also available for free. Plus, it's web based so works everywhere. Last but not least, it has programmimg (pine) support for backtesting and custom coding your indicators and strategies. You can have your personalized setup and everything is saved in your account so you can access it and trade from anywhere. It also lets you paper trade.

Other popular charting software include Amibroker and Metastock. In terms of features, they probably have everything you would even need, including F&O, option chains, OI analysis, backtesting and so much more. Amibroker is arguably the better option but the issue is that they work only on Windows. If you're on Mac or use a linux flaour (e.g. Ubuntu) then it won't work. 

TradingView has an option to you save screenshot of your charts which you can insert in the posts. I have inserted a screenshot of BankNifty futures hourly chart below as an example.