«Красивый» is 'beautiful', it refers to aesthetics. «Прекрасный» means it's very good, but not neccessarily because it's beautiful. For example, «она́ прекра́сная программи́стка» 'she is a wonderful programmer' means she is a very good programmer, and «краси́вая» wouldn't work in this context.
Not even as a compliment? Meaning, she is a beautiful programmer, on behalf of her looks.
No, «прекрасная программистка» would mean she writes code well, it can't mean she's beatuful. But I think this is also a compliment, isn't it? I mean, I think when someone compliments a person's work, it's as much a compliment as when they compliment someone's looks, isn't it?
«Она красивая программистка» could mean she's a beautiful programmer, but in Russian this sentence sounds pretty strange because Russian prefers not to pack different messages into one sentence. It's better to say «Она программистка, и она красивая» 'She's a programmer, and she's beautiful'.
And could I use "красивы" to describe the personality of someone? Like "Tom Hanks is a beautiful person" in the sense that he is really kind.
Oh well... Techically it could mean this, but this is bound to be misunderstood. Unless you have a context where it's obvious. E.g. you've discussed how appearance is not important for you before, and now you say «Том Хэнкс — красивый человек», then it could be understood to refer to inner beauty.
But if you just say «Том Хэнкс — красивый человек», without any context, it would be understood as a sentence about appearance ('Ton Hanks is a handsome person.').
You could add more words to clarify you're not talking about appearance, e.g. «красивый душой человек» 'a person beautiful in soul', «красивый внутренне человек» 'internally beautiful person', etc.
The word 'splendid' has not entirely fallen out of use in American English. As a native speaker, I use it and hear it used occasionally - and not in a contrived way, but as part of natural speech. It's not the most commonly used word nor the rarest. Splendid could certainly be used to describe a garden - but a grand one (великолепный сад). 'A lovely (or fine) and quiet garden' would be a good translation of прекрасный и тихий сад.