How are option values calculated?
Option values are calculated using the Black-Scholes equation.
Why does my broker or another data source have different option prices?
Options prices are as close to real time as possible but are not always accurate. Furthermore, the accuracy of options data and other pricing data is dependent on our data sources which themselves are not guaranteed to be always accurate. Finally, prices are dependent upon market conditions which are constantly changing. Information here is just an estimate and does not constitute investment advice.
Why did the output of the calculator change or why did it not match what actually ended up happening?
Implied volatility is an input in the Black-Scholes options calculation and is not constant. Earnings reports and company statements may cause drastic changes in the implied volatility which impacts the accuracy of the calculations.
Does the get stock price feature take into account after market close price changes?
No. Stock prices update (often with a 15 minute delay) when option markets are open only. However, the charts show the estimated option price at a certain strike price on a certain date, so you should be able to see the estimated option price at market open the next day.