Complex bundles and (quasi)-complex structures of manifolds

Question

Could you help me with some hint or reference for the following questions?

I'm reviewing the Milnor-Stasheff for references.

1. Is there some $(2k)$-manifold with stably quasi-complex structure, such that the structure is not complex?

2. Is there some $(2k+1)$-manifold that is stably quasi-complex?

3. Is there any embedding of $\mathbb{CP}^4$ in $\mathbb{R}^{11}$?

4. For which values of $n$ does it have that $\mathbb{CP}^n$ has structure Spin?

Where,

a) Let $ E \rightarrow M $ real vector bundle of range $ 2n $, a quasi-complex structure in the bundle is a function $ J: E \rightarrow E $ which is $ \mathbb{R} $ - linear in each fiber and such that $ J \circ J = -Id $

b) Stably quasi-complex structure for $M$ means that there exists a trivial vector bundle $ \eta: \mathbb{R}^k \rightarrow M $ such that $ \eta \oplus \tau M $ (the Whitney sum of bundles) has a complex structure for $ M $ (with $\tau M$ the tangent bundle of $M$).

First of all, Thanks