Which is fine. Whom is the objective form of who. In English, the dative and accusative merged into the objective case, which hasn't happened in German.
One could view whom and who in the same way as one would look at him and he. For example, you wouldn't say ''The dress belongs to he'', but ''The dress belongs to him''.
This is an old myth, and it leads to some terrible writing. English is not Latin, and trying to insist that English should follow Latin rules is quite as silly as insisting that English should follow the grammar of French. In English, prepositions often do fall naturally -- and correctly -- at the end of the sentence.
Here is the Oxford English dictionary on the history of this awkward dictum, giving examples showing why it is bad and wrong. https://blog.oxforddictionaries.com/2011/11/28/grammar-myths-prepositions/
If you put 'To Whom' at the start of your sentence, there is no need to put 'to' at the end of your sentence. "To whom does the dress belong?" is the same as "Whom does the dress belong to?"
Now, Duo might be messed up and wouldn't accept either, but the two examples above are correct in terms of English grammar.
"Excuse me, I don't know who to give this to" is grammatically correct far outside of the American south. There are exceptions to practically every "rule" in English grammar. "Where does that road lead to?" is also correct. Granted, both of these could be reworded to avoid the "to" at the end of the sentence, but that doesn't make them incorrect.
Except grammatical rules. You can choose not to follow them and this particular one is very commonly broken and to the extent that many consider it to no longer be required. My personal preference is to seek to follow grammatical rules where i know them. It seems everyone is very keen to follow them when learning a foreign language but less interested when they relate to their own language. The argument that it is correct to put 'to' at the end of a sentance because it's common isn't a very strong one - everyone believing the same mistruth doesn't make it true. Just my opinion.
In most cases, it's a myth that ending a sentence is grammatically incorrect: https://www.grammarly.com/blog/youve-been-lied-to-heres-why-you-absolutely-can-end-a-sentence-with-a-preposition/ There are lots more articles about it, google it.
"Whom" is vanishing in English, but either "who" or "whom" would be normal here - and "whom" is formally correct. See: https://en.oxforddictionaries.com/usage/who-or-whom
Indeed; strictly speaking, 'who' is a subject pronoun, 'whom' an objective form, comparable to 'he' and 'him', 'I' and 'me', etc. 'Whom' is generally replaced by 'who' when it stands at the beginning of a sentence or clause. Although this is deprecated by some people, but I think is only a problem in the most formal writing/speech. But as the subject of a following verb: 'the woman whom I said would be waiting for you' for example, the 'whom' here should read 'who' as it is not the object of 'said' but the subject of 'would be waiting'. Removing 'I said' makes it a little clearer.
You're thinking of the verb "hören," to listen, hear; gehören, to belong to, is derived from hören, to hear, listen to. My belongings listen to me? But then, in English, apparently my belongings long for me... Looking it up on wiktionary, it seems that my belongings concern me, so perhaps in German, one listens to ones belongings: https://en.m.wiktionary.org/wiki/belong