Implied volatility vs delta

The clasification of options between out-of-the-money, in-the-money, and at-the-money will be a determining factor in properly applying the extraction methodology and obtain meaningful results for different options monsters. After some python experimentation, the dataset is ready to be analyzed and available for calculations. My question today revolves around the the mening of the obtained graf in delta vs. volatility space.

The shape from the graph makes sense, since delta values for calls and puts are positive and negative. Volatility is positive since is the percent change and is provided by the courtesy of Yahoo! finance. On this note, I will spend some time in finding out two things:

1. How does yahoo! finance calculate implied volatility? (probably BS!)

2. What Risk free rate do they use for calculations?

Literature and internet review showed that many people that deal with the BS formula omit the discussion about the risk free rate and its estimation or use. Given that IV is provided, one can extract the risk free rate from it. Once I compounded the BS formula with D-parameters, I came to find out that this will not be a simple task to do. The r parameter is found both in the original equation and in the proces of calculating the normal distribution. Have fun whomever will decide to figure this out!!! :)

Lastly.... from one paper where deltas and implied volatilities are plotted, only positive deltas are used for both calls and puts that are out-of-the-money. Were deltas put in absolute values to extract the estimation function?