I think "When do you begin the presentation?" and "When will you begin the presentation?" mean the same thing in English.
Yes, true, hard to argue with that. However... we prefer to separate 'Present Continuous (and sometimes Simple) in the future meaning' from normal Future Tense. Why? Well, in English you immediately see which one is Present Tense and which one is Future Tense. No room for a mistake, if only you know the very basics of the language. But in Polish, if you're just a learner, it's not that obvious that "zaczynasz" is Present Tense (used in the future meaning here) and "zaczniesz" is the real Future Simple. Because of that, we keep to the tense used.
Is an implied possessive allowed here? "When do you start your presentation?"
Sure, it works. But logically, who else's presentation you can start rather than yours? ;)