Recently studied some variations for this corner shape. Here are some puzzles. Stronger players than me may already know them by heart.

Edit: tweaked surrounding stones

Click Here To Show Diagram Code

[go]$$ Black to play, status?
$$ --------------------
$$ | . . . . X . . . . .
$$ | O . X X O O . . . .
$$ | . . X O . . O . . .
$$ | . X X . O . . . . .
$$ | X O O O . . . . . .
$$ | . . . . . . . . . .
$$ | . O . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$ Black to play, status?
$$ --------------------
$$ | . . . . X . . . . .
$$ | O . X X O O . . . .
$$ | . . X O . . O . . .
$$ | . X X O . . . . . .
$$ | X O O O . . . . . .
$$ | . . . . . . . . . .
$$ | . O . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

Click Here To Show Diagram Code

[go]$$ Black to play, status?
$$ --------------------
$$ | . . . . X . . . . .
$$ | . . X X O O . . . .
$$ | O . X O . . O . . .
$$ | . X X O . . . . . .
$$ | X O O O . . . . . .
$$ | . . . . . . . . . .
$$ | . O . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

The L+1 shape with extra hane on both sides is essentially alive, if I remember correctly. It is alive with territory if there are extra outside liberties, as in your first diagram.

With no outside liberties, the best attack is probably the placement in your second diagram. I think this leads to mannen-ko, which is not completely alive but is usually impractical to kill:

Click Here To Show Diagram Code

[go]$$W
$$ --------------------
$$ | 7 6 . 2 X . . . . .
$$ | 1 5 X X O O . . . .
$$ | . . X O . . O . . .
$$ | 4 X X O . . . . . .
$$ | X O O O . . . . . .
$$ | 3 . . . . . . . . .
$$ | . O . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

I think the placement in your third diagram lets B live with territory through double ko, starting like this:

Click Here To Show Diagram Code

[go]$$W
$$ --------------------
$$ | . 4 . 5 X . . . . .
$$ | 6 3 X X O O . . . .
$$ | 1 . X O . . O . . .
$$ | 2 X X O . . . . . .
$$ | X O O O . . . . . .
$$ | . . . . . . . . . .
$$ | . O . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

I've been studying the L and L+1 groups too!

mitsun gave answers for the last two of the three problems. Here's my attempt at the first one:

What about this?

-> seki

So W has a choice and leaves the position until endgame. This gives him an infinite number of 20 pts ko threats. Correct?
I think it also means that defending the L+1 with two hanes in order to keep sente is quite dubious.