I tried looking this question up on google and didn't find material that answered my question. But my questions are:

(1) Is there a method to determine how long it takes a leading indicator to affect a variable ? So if we are looking at the affects of oil production on sales, when oil drops how long does it take to affect sales.

Could I use survival analysis for this? This seems related but in a biological context

(2) Can we measure the degree to which oil production affects sales? If oil production drops by 10% it affects sales by 17%.

(3) What's the best way to determine the most important leading indicator? Univariate regression and compare models?

(4) Is there a package in R that could be used for this?

(1)To find lead/lag indicator time Cross Correlation Function can be used in R with the ccf command.
(2)To find the effect of the indicator $x_{(x+h)}$ on $y_{x}$ you can regress on the lag function and use the coefficient $\beta_{1}$ in the regression as the magnitude. As found here