You are right, entangle returns tensor product of two vectors indeed.

Edward Kmett is magnificent. When we discussed the original article in Russian, this question arose once. Of course one need to use good linear-algebra-library, if he want to implement QC framework.

No, you can't. But you can use the values from that outputs in other gates.

Not really necessary. Often we can drastically optimize the number of used gates, and the «gibberish» outputs can be used in other computations.