You will need to make sure that you are using the Maple-graded response area with Maple Syntax on. From there, the grading code depends on how you expect students to enter their response.

Part 1) Text Entry: I assume that you have a working variable $v for the LinearAlgebra[RandomVector] command. If students enter [1,2,3] then use the grading code

u:=Vector($RESPONSE); evalb($v.u=0);

Part 1) Symbolic Entry: Similarly, where $v is the random vector, the student uses the Matrix/Vector entry button, then use the grading code

u:=convert($RESPONSE,Vector); evalb($v.u=0);

For 2), you just need to test that the two vectors in the basis are orthogonal and both satisfy the equation of the plane, correct? Suppose $plane represents the equation of the plane without z (e.g. $plane=3x+2y). In Symbolic mode, if the student enters both vectors separated by a comma, then try this:

r:={$RESPONSE}; evalb(eval($plane, [x = r[1][1], y = r[1][2]]) = r[1][3] and eval($plane, [x = r[2][1], y = r[2][2]]) = r[2][3] and u.v = 0);

If this does not help solve the issue, I would suggest exporting the question as you have designed it currently, and attaching the zip file here.