I'm using the app, so I can't tell how 'old' your question is... Also I'm not a native. But here's how I understand it: Some verbs that use się do not take an object - for example urodzić się. Other verbs that use się DO take an object - for example podobać się like in this sentence, the object being a personal pronoun in the dative case, mi. (Someone correct me if that was wrong please)
You are absolutely correct, "podobać się" needs an object. Ex. I like this = To mi się podoba. Asking "Czy twoja sukienka się podoba?" would have quite a different meaning: "Is your dress liked (by everyone)? So, it is possible but not very common to NOT have the object here.
Yeah ... 'podoba mi się' can be quite a difficult phrase to translate to/interpret in English, whilst conveying the appropriate meaning, according to the context of the rest of the sentence. For some of the Polish sentences on Duo 'appeals to me' is accepted as a translation. But I do agree that in this context 'Your dress appeals to me', would be an odd/unnatural thing to say someone, even if it does make sense in English.
Mi podoba się... doesn't work, because you can't start a sentence with an unaccented object pronoun (however, some natives do it anyway).
Technically, Podoba się mi... is correct, but a search in the National Corpus suggests that this word order is almost 60 times less common than Podoba mi się.... Hence, I won't accept it for now, but I'll ask the team to confirm this decision.
Now, with nouns, it's a bit different. I've searched the corpus for sentences that start with:
1) [Noun] + się + [podobać] -> 27 results.
2) [Podobać] + się + [noun] -> 51 results.
3) [Noun] + [podobać] + się -> 80 results.
4) [Podobać] + [noun] + się -> 0 results.
So, I'd say that only Podoba się Janowi..., Janowi się podoba... and Janowi podoba się... are acceptable options.