Are $\mathbb{Z_p},\mathbb{Q},\mathbb{R},\mathbb{C}$ above themselves vector space?
Is a field above anoother field a vector space?
As for 1. we know that $\Bbb R^n$ is a vector space so in particular it is true for $n=1$
For 2. by definition a vector space is $V$ with addition and multiplication over a field, therefore 2 is true.
A vector space is a set with an addition law and a scalar multiplication law, where the scalars are elements of a field. Thus, a vector space over a field may not be itself a field (e.g. continuous functions on an interval); however, a field is always a vector space over itself. Similarly, taking direct sums of a field will give you a vector space over the original field (e.g $\mathbb{R}^n$ is a vector space over the field $\mathbb{R}$).