Questions & Answers about Was ist heute das Datum?
Is Was ist heute das Datum? the most common way to ask for the date?
It is perfectly understood, but Germans actually prefer to ask Der wievielte ist heute? (literally: the how-many-th is today?) or Den wievielten haben wir heute? (the how-many-th do we have today?).
How do I answer this question using an ordinal number?
Because the sentence uses the verb ist, your answer will be in the nominative (subject) case. For example, you would say: Heute ist der vierte Mai (Today is the fourth of May). Notice the ordinal number ends in -e here, not -en.
Since we are learning about using am for dates, should I answer this question with am?
No! You only use am (which changes the ending, like am vierten Mai) when answering the question Wann? (When?). Since this sentence just asks what the date is, not when an event happens, you do not use am in your reply.
Can I change the word order to Was ist das Datum heute?
You will be understood, but Was ist heute das Datum? sounds much more natural. In German, time words like heute usually prefer to sit right after the conjugated verb.