Finite co-dimensional Banach spaces and some bounded recovery problems

(1) If Y is a finite Co-dimensional subspace of a Banach space X and Z is its complementation, is for every projection P0 from X onto Z and every 2 > 0 there a projection P from X onto Y satisfying (1) ‖P‖ ≤ 1 + (1 + 2)‖P0‖? (2) If X is a Banach space, x ∈ X, Y is an n-CO-dimensional subspace of X and ({fi, xi}i=1) is the Auerbach system of the complementation Z of Y in X, is there an element y ∈ Y satisfying the following two conditions