1.
a is very big but it is possible to tenuki if there is an even bigger move elsewhere. It builds territory on the left and also helps take care of bad aji in the corner (white has moves like 3-4 attachment or 2-4 submarine). If white gets it then she builds influence on the left and it's harder for black to fight the ko at the top as his corner gets sad if he loses it. Also it keeps open possibilities to attack white's group later with a pincer on the top side if she fails to make an extension, though the ko complicates this. A very multi purpose move.
2. Both could be possible but
a is solid honte style that attacks the group as a whole and prevents white pressing black down in sente. If
b the expected continuatuon is (maybe 5 one below or try peep first):
- Click Here To Show Diagram Code
[go]$$B
$$ -------------------------------
$$ - . . . . . . . . . . . . . . .
$$ - . . X . . . . . . . . . . . .
$$ - . . X O O . 1 . . X . c . . .
$$ - . . 3 X 4 . . a . . . . . . .
$$ - . . 5 2 . O . . . . . . . . .
$$ - . . . b . . . . . . . . . . .
$$ - . . X . . . . . . . . . . . .
$$ - . . . . . . . . . . . . . . .
$$ - . . . . . . . . . . . . . . .[/go]
White may then press at
a, run with some other move, can make eye shape with b or even pincer the top group at c depending on the situation. Black loses quite a few points and thickness in sente this way. It depends a lot on the top side situation. Something to note is with honte answer white has a shape problem at
a after extending so it's honte for her to defend at
b:
- Click Here To Show Diagram Code
[go]$$B
$$ -------------------------------
$$ - . . . . . . . . . . . . . . .
$$ - . . X . . . . . . . . . . . .
$$ - . . X O O . . 2 . X . . . . .
$$ - . . . X . . a . . . . . . . .
$$ - . . . 1 . O . b . 3 . . . . .
$$ - . . . . . . . . . . . . . . .
$$ - . . X . . . . . . . . . . . .
$$ - . . . . . . . . . . . . . . .
$$ - . . . . . . . . . . . . . . .[/go]
3. Yes but then black will likely capture the cutting stone on the outside in a ladder or net which defeats the purpose of cutting in the first place. Atari is a thank you move.
4. a is amore severe shape attack and is better placed in the sequence below. Also black hasn't fixed his cut on the left so must be careful.
- Click Here To Show Diagram Code
[go]$$B
$$ -------------------------------
$$ - . . . . . . . . . . . . . . .
$$ - . . . . . . . . . . . . . . .
$$ - . . . X O O . . b . . . . . .
$$ - . . . X . X O . 1 . . . . . .
$$ - . . . . . X 2 . . . . . . . .
$$ - . . . . . . 3 . . . . . . . .
$$ - . . . . . . . . . . . . . . .
$$ - . . . . . . . . . . . . . . .
$$ - . . . . . . . . . . . . . . .[/go]
5. Typo? Black should play the other 2-1 point.