"euch" is the accusative form of "ihr" , the nominative form of plural informal or familiar "you". euch never means her (I reported this for you.), but "sie" becomes "ihr" in the dative form. ( not the genitive form but the possessive form see TrioLinguist below)
Here is a site that lists all the forms for each case for all the pronouns.
"sie" becomes "ihr" in the dative form and genitive form.
You're right about the dative being ihr, but it's the possessive form that's also ihr (e.g. das ist ihr Hund), not the genitive pronoun which is ihrer, which is only used in the event of a genitive object, for example:
- Poseidon erbarmte sich ihrer - Poseidon had mercy on her
- Du bist ihrer nicht würdig. - You're not worthy of her
Note that genitive pronouns are rare because genitive objects are rare, since genitive is mainly used after prepositions and to show relation between nouns nowadays. They are only commonly found in poetry, but also occasionally in literature and formal writing.
Yes, exactly, du is the one that does the liking and dich is the one being liked.
Both statements and questions can make use of grammatical cases. It depends on the question word to be used if the statement would be turned into a question:
- Wer? - Nominative
- Wessen? - Genitive
- Wem? - Dative
- Wen? - Accusative
The sentence "Ich mag euch." could be transformed into a question as "Wer mag wen?". Subject (who?) likes the object (whom?).
Please read some grammar documentation to learn more about grammatical cases:
Because that's nominative, it's like how you can't say I like he in English, you have to use the accusative form, which is him. Same concept here – you need to use the accusative form of ihr which is euch.
Du/dich would be fine but remember that refers to one person, while ihr/euch is plural.
I knew what was meant, but since English doesn't really have a fully accepted plural version of "you", I put "y'all", which is counted as correct. In my dialect of English I'd normally put "You'ns" (You ones), but choose not to put that here as it's less recognized than "Y'all", which was accepted.