Can somebody explain why we don't use "Italion" here? There is motion towards a place. I appreciate it!
You can say "Kiam ili iros al Italio" or "Kiam ili iros Italion", but not "Kian ili iros al Italion", because -n use to replace "al" or "gxis". It is kind of redundant to denote the movement with -n and also with "al".
Because it is being used with the preposition 'al'. In Esperanto the accusative ending is not used when the noun is preceded by a preposition. EDIT: Disregard that, I just read the note about the accusative with prepositions indicating motion. I'm not sure why there is no ending in this instance. My best guess would be that 'al' always indicates motion whereas other prepositions could be ambiguous, e.g. 'sur' could mean 'on' or 'onto' and 'en' could mean 'in' or 'into', so the accusative case serves to clarify.
Using -n with certain prepositions is just a grammatical trick. Some prepositions could be used to indicate an action and a change. You don't want those two to be the same, so you use a trick to keep them different. In English, you e.g. add "to": the action "I walk on the ice." is not the same as the change "I walk onto the ice.". Esperanto also uses such a trick, again just when a proposition can be used for both an action and a change. But Esperanto does the trick with the "-n". If it's an action, nothing happens, but if it's a change, you get -n.
But, remember this is only for when a proposition can be used for both an action and a change. Now, "al" can only be used for a change, thus it's not one of those prepositions that sometimes result in "-n".
"When are they going to Italy?" <-- I'm not sure I fully understand what is wrong with that sentence.
Your sentence is incorrect because it is still the present tense.
"Kiam ili iras al Italio" is how you would say "When are they going to Italy"
Kiam ili iros al Italio" is only the future tense, and must either be "When are they going to go to Italy?" or "When will they go to Italy?"
How about "When will they be going to Italy?" The will is used as a future marker often.