The difference in English is apparent and used to imply things, like you say, but in other languages (e.g. Italian, Spanish, German) it isn't so apparent since none of the words change and thus one sentence in Italian can imply two different things in English and still be correct.
In my opinion "why hit your brother" is an acceptable alternative to "why do you hit your brother". It perhaps has a looser meaning, eg the former could imply a potential future action (why do you plan to hit your brother), while the latter clearly refers to a present or habitual action, but it can also mean exactly the same. I'm not good enough at Italian to know if this is significant, but it seems very unlikely.
As for #1 there is a discussion above; this sentence translates the same, or you could use "perché stai colpendo tuo fratello?" to stress that the action is happening at this very moment.
Now, #2 is more interesting: all Romance languages inherited a sound shift that occurred in late Latin (probably from Celtic influence) that caused "ce" and "ci" to be pronounced differently from "ca", "co" and "cu" (here there is a discussion). English also inherited this spelling from the Normans, and that's why the C in "call" in pronounced K while the C in "cell" is pronounced S. In Italian the C before E and I is pronounced like the English "CH", while SC before E and I is pronounced like the English "SH".
That would be "Perchè hai colpito tuo fratello" so in this case "hai" (avere) does (kind of) the same thing as "did", but some verbs require "essere" instead of "avere", so it's a bit more complicated than in English. Plus the verb itself takes a different form (colpisci --> colpito)