In the book 'Open Problems in the Geometry and Analysis of Banach Spaces', I am interested in the following two problems.
Problem $1$: Let $X$ be a separable infinite-dimensional Banach space that is not isomorphic to a Hilbert space.
(i) (A. Pełczyński) Does there exist an infinite dimensional subspace of $X$ with Schauder basis that is not complemented in $X?$
(ii) (A. Pełczyński) Do there exist two infinite-dimensional subspaces of $X$ with Schauder basis that are not isomorphic?
I would like to know status of the two problems above. Are they solved or still open?