aní ochél beitzá.
Should "I am eating egg" be acceptable here?
Nouns seldom go without an article in English, so "an egg" is probably a more correct translation.
I think so.
I don't think so - unquantified egg is much more likely to translate into the plural in Hebrew - ביצים
Beitsah = egg
Is "I eat an egg" and "I am eating an egg" be expressed in Hebrew the same way?
Yes!
Why do I need an before egg?
because it's an indefinite single object