Entanglement of 3-qubit states

Question

Given a separable 3-qubit state

φ = φ₀ ⊗ φ₁ ⊗ φ₂

with

φ_i= a_i0|0> + a_i1|1>,

|0>, |1> being the computational base. φ thus can be written as

φ = b₀₀₀|000> + b₀₀₁|001> + b₀₁₀|010> + b₀₁₁|011> + b₁₀₀|100> + b₁₀₁|101> + b₁₁₀|110> + b₁₁₁|111>

with

|ijk> = |i> ⊗ |j> ⊗ |k>

b_ijk = a_0ia_1ja_2k.

---

Now let some b_ijk be given, defining an arbitrary 3-qubit state

φ = b₀₀₀|000> + b₀₀₁|001> + b₀₁₀|010> + b₀₁₁|011> + b₁₀₀|100> + b₁₀₁|101> + b₁₁₀|110> + b₁₁₁|111>

Question 1

How is Schmidt decomposition to be applied to the tensor B = (b_ijk) to find out if the state is separable?

Question 2

Assuming that the following five possibilities of entanglement are possible

1. φ₀, φ₁ and φ₂ entangled,

2. φ_i separable, φ_j and φ_k entangled,

3. φ₀, φ₁ and φ₂ separable,

how do I calculate the corresponding coefficients, i.e. in case (3)

φ = φ₀ ⊗ φ₁ ⊗ φ₂.

where I want to know the six coefficients a_ij in

φ_i= a_i0|0> + a_i1|1>.