Well this is a nice game but I think a lot having issue is probably due to the MTL. As for going to the heroines events, look at the details when you check on each info. Some is quite straight forward but a few will need some of them to reach a certain level liking before things will continue (Which is Harry, Gordon, Grace and Kate). A few will need to have given birth at least once. For Liliel (リリエル), she will need to be in prenancy status for things to continue.
I had read through all the comments here earlier and this "Anyone has a idea of how the Archievement "All villagers have a children in one day". works?" is likely a translation error. Anyway, that achievement is translate as making a baby with every village (except male, old and young) in 1 day. Which meant, do it with everyone except Harry, Gordon, Grace and Kate. This one is very easily to get once you marry all 16 which is also part of the achievement and do it on a Monday as all of the heroines except for 1 or 2 will not be at your home at 6am when the day reset.
1 month have 30 days for 4 seasons. Each week have 6 days (Monday to Friday plus Rest day)
The ranch girls are divided in 3 types, 1 that gives eggs which have also 3 types of eggs, 1 that give milk which a have 3 types of milk and finally 1 that gives fur which have 2 types of fur. Furthermore, if the ranch girls give birth 3 times or more and the likes are max at level 8, they will give the best of their stuff which actually sell for a lot more than usual.
As for their most favourite thing. A clue actually is given in what they like and compare it to the list of cooking ingredients. It will let you know which is which but I already saw someone post up the list here, so just follow that will do. Giving them what they like will net either 5 or 10 like points but I am not sure of most favourite thing though as I already max out all that when I was doing that achievement. Giving them what they don't like will get 1 point of like point. But the best way to get it is just greet them per day (get 3 points) and talk to them which get 2 point but can repeat to get every change of time in 3 hours. And doing events can either get 0, 10 or 20 points. But note, the 3rd event to get laid is usually worth 20 point and the last event before able to get marry is also worth 20 points.