Are those statements corrected:

The Hibert space of a composite system is a vector product of Hibert space of the subsystems.

To find the matrix representation of a two-qubit gate composed of two single-qubit gates one needs to calculate the tensor product of the mentioned two single-qubit gates matrices.

If you separate two entangled systems over a distance you will reduce their entanglement level.

A 3-dimensional quantum system (also referred to as a quirt) can be defined as a superposition between 3 orthonormal vectors of the basis.