Is this corner dead?
Since T14 allows a sente hane, the initial board effectively looks like this:

$$W
$$ ------------|
$$ . X O . . . |
$$ X . X O . . |
$$ . . X O . . |
$$ . . X O O . |
$$ . . X X O . |
$$ . . . O X 1 |
$$ . . . X 2 . |
$$ . . . . . . |


The usual attempt is to hane from the outside, then kill by playing at the vital point:

$$ ------------|
$$ . X O 4 3 . |
$$ X . X O 7 2 |
$$ . . X O . 6 |
$$ . . X O O 5 |
$$ . . X X O 1 |
$$ . . . O X 8 |
$$ . . . X . . |
$$ . . . . . . |


But after 8, play cannot play at 1 to remove the eye due to atari.

Let's try a vital point in the corner directly:

$$ ------------|
$$ . X O 6 . 8 |
$$ X . X O 4 1 |
$$ . . X O . 5 |
$$ . . X O O . |
$$ . . X X O 7 |
$$ . . . O X 2 |
$$ . . . X 3 . |
$$ . . . . . . |


After 8, the situation becomes a 2 step ko in b's favor.

Next, consider this sequence:

$$ ------------|
$$ . X O . 4 5 |
$$ X . X O 1 2 |
$$ . . X O . 3 |
$$ . . X O O . |
$$ . . X X O . |
$$ . . . O X . |
$$ . . . X . . |
$$ . . . . . . |


After B5, the position is a direct ko. Black wins the ko by playing at 2, creating a dead shape inside. The same position arises if B1 is at B3.

However, thanks to the marked stone, black should try this:

$$ ------------|
$$ . B O 6 5 . |
$$ X . X O 1 4 |
$$ . . X O 9 . |
$$ . . X O O 8 |
$$ . . X X O 7 |
$$ . . . O X 2 |
$$ . . . X 3 . |
$$ . . . . . . |


The shape is dead without ko.

In the original diagram, black can still aim for the same shape:

$$ ------------|
$$ . X O O X . |
$$ X . X O 1 . |
$$ . . X O 5 . |
$$ . . X O O . |
$$ . . X X O 4 |
$$ . . . O X 2 |
$$ . . . X 3 . |
$$ . . . . . . |


After B5, white is short of liberties and dies.