Re: Sim being sad from 'close sentiment towards someone feeling bad'
I get this a lot, particular with families and it can be set off by anything. Like @PipMenace says the other Sim can get over their issues but their loved one has the moodlet for a while. I often get it just because a Sim really needs a shower and is uncomfortable say if they've been working out and feel grungy. It can be because they've just got out of bed really hungry and even after they've solved their need they still have a parent who is over empathizing and sad. It happens more for me with Good or Family Oriented Sims.
The sadness moodlets have needed work for a while. There are too many of them and they are way too buggy and nonsensical.