It is known that a finite dimensional basic algebra over an algebraically closed field is isomorphic to the path algebra of a finite quiver modulo an admissible ideal.

Question 1: Is the same true for algebras over $\mathbb{Q}$? If not, are there suitable further assumptions that would guarantee this?

Question 2: Are there some general useful tools to compute the dimension of the algebra, given the quiver and the ideal? (In concrete, easy cases it might be doable by hand, but I am looking for methods that are more broadly applicable)