There is no weather facility anymore in this version of the game, that thread is more than 2 years old.
To find out how long it will rain check the weather at the race track in reality, especially weatherunderground.com will be usefull there because that's where the games weather information comes from. Bear in mind though that the weather is updated every 10 minutes or so and thus the length of a weather phase might differ by about that amount of time in the races.
When is a bit more difficult. As said the game is updated every 10 minutes and that's about the first delay, you can see in the games weather forecast window (https://igpmanager.com/app/d=forecast&trackId=
X with X replaced by the number of the seasons race you want to check) when the core games weather changes. But then there's a second delay between the core game and the race viewer session and that differs from about another 10 minutes to 20 or even 30 minutes. You'll have to figure out yourself by what amount your league and tiers race weather lags behind. It (usually) doesn't change that much between different races, at least not in the leagues I participated in, but it's not that exact to calculate a certain lap.