Learning new vocabulary is great! However, don't forget to learn how to actually apply the word into a real life setting. Remember: context is key.
I care about my education.
All of those sentences use perfect English… for the classroom. In real life, people don't actually use those expressions. They can, but it would be a little unnatural.
The reason is that we more commonly use "care" in response to an argument. If someone accuses us of "not caring", we can quickly retort back "We do care!" Yes, it's really that simple.
But Jon, you might say, I've been hearing politicians say "they care~" about so many things on the news.
Remember: context is key. In those situations, are they normal conversations? No. They're elevated platforms in which the candidates are supposed to argue a cause. They're in effect very formal.
For the rest of us? We'll save the word "care" for our dating lives.