Sounds like you got that ancient curse, "May you live in interesting times."
Go to Gameplay options and you'll see Allow Romantic Invites and Requests. Turning that off should stop NPCs from proposing. If you leave it on, proposals are pretty common after successful dates if both Sims are single. The proposals can get annoying, especially if you're playing the Serial Romantic aspiration.
I've never had a Sim drop dead from rejecting a proposal but I suppose it could happen. The Sims 4 has some emotions that can cause death and Embarassment is one of them.
Try For Baby unlocks at the same relationship level as Woohoo. It doesn't cause adoption but it might cause pregnancy, so you may get another phone call in a few days to let you know a child was born.
The adoption message was just a coincidence, I'm sure. Adopted Sims can range in age from Newborn to Child, so the adopted Sim might have been a Child and off at school or somewhere else. You can stop adoptions by turning off Neighborhood Stories under Gameplay options. You might need to scroll down to find the option. You can also stop adoptions by changing the Neighborhood Stories settings in Manage Worlds/Manage Households.
I don't think you need mods, although there's nothing wrong with using them. I've been playing TS4 since it was released, over 10 years ago, and I've never had any mods. Based on what I've seen in the various forums, I experience a lot fewer bugs than the players who do use mods.
