A silly doubt on Computer Science Objects: Arrays, Lists, Strings, and Vectors, are they the same concept?
The objects you mention are not the same.
In particular, lists and (mutable) strings are dynamic data structures whereas arrays are not; their size is fixed.
Now, whether some set of instances of data structures forms a vector space depends on the underlying types, some do, others do not.
Considering e.g. boolean arrays of fixed size $n$ together with the usual addition/scalar multiplication of $\mathbb F_2^n$ yields a vector space, integer arrays of fixed size $n$ do not yield one with the usual operations.