Translation:I cannot relax!
放心 is more like to be at ease, in which you don't feel worried over present obstacles
Yes. Since the context is not clear in terms of the sentence's meanings, the correct translation can also be
which literally means that one cannot "rest".
I totally agree. "放松" would be a better choice, but I would only think of it in the context of relaxing your body or mind. "休息" is another good option, however, I normally use it when someone is working hard & deserving of rest, or napping."