1. e4 c5 2. Nf3 Nc6 3. Nc3 Nf6 4. e5

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Q1: Does it have a name?

Q2: Do you know where to find some theory about it?

Q3: Do you ever see it on the board?

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Ok, here are a couple of games with decent players.
 

As to your comment about 3... Nf6. Well. People do play 3... Nf6. And it seems pretty clear to me that you are not competent enough to say that "black has so many better moves" - even I know that this is very far from truth.