Its ability to feedback (3) allows it to execute algorithms, but only a certain class of algorithms. Without tailored prompting, it's further restricted to (a weak generalisation of) algorithms spelled out in its corpus. This is very cool, but this is a skill I possess too, so it's rarely useful to me.
Its ability to plagiarise (2) can make it seem like it has capacity that it doesn't possess, but it's usually possible to poke holes in that facade (if not even identify the sources it's plagiarising from!).
It is genuinely capable of explicit translation (1) – though a dedicated setup for translation will work better than ChatGPT-style prompting, even on the same model. A sufficiently-large, sufficiently well-trained model will be genuinely capable of translating idiomatic language (for known idioms), for the same reason it can translate grammatical structures (for known grammar).
It can only perform higher-level, "abstract" translations – like those necessary to translate a Phoenix Wright game – if it's overfit on a corpus where such translations exist. (https://xkcd.com/2048/ last graph) This is not a property you want from a translation model: it gives better results on some inputs, sure, and confident-seeming very wrong results on other inputs. These are two sides of the same coin (2).
When the computer can't translate something, I want to be able to look at the result and go "this doesn't look right; I'll crack out a dictionary". I can't do that with GPT-4, because it doesn't give faithfully-literal translations and it isn't capable of giving complete translations correctly: it's not fit for this purpose.