Eigen does compile-time detection of the SIMD engine it will use, but it's possible to disable that with the flag `-DEIGEN_DONT_VECTORIZE` passed to the compiler.
Matrix is the generic class, Vector is the 1D special case of the Matrix, and Tensor is currently in the `unsupported` directory of Eigen.
Yes, in general, code that involves calculations with vectors, matrices, and tensors benefits from larger vectors - this is why the A64FX SVE CPU uses 512-bit vectors.