Ex(n,P) Bounds and Questions

Here is the place to put all $$ ex(n,P)$$ bound values and all open and closed questions about $$ ex(n,P) $$. Please note if they are closed or open.

Bounds on ex(5, L2)
Let L2 be the matrix:

0 1  1  1  0

1 0  0  0  1

0 0  1  0  0

Lower bound: 14

Start with a 5 x 5 matrix with every entry equal to 0. Change every entry in the top 3 rows to 1 except for the middle entry in the third row. This matrix has 14 ones but avoids L2.

Upper bound: 22

Any 0-1 matrix of dimensions 5 x 5 with 23 ones contains a 3 x 5 submatrix of all ones.

Open Questions
If P is a 0-1 matrix of dimensions m x n with m < n, then what is the value of ex(n, P)?

For each positive integer k > 1, 0-1 matrix P, and positive integer n > 0, what is ex(n, P) (mod k)?