A few answers from looking at the game with Lizzie:
Ian Butler wrote:1) Move 15: is it bad?
Lizzie thinks your move is better than the joseki move by 3%. However, Lizzie prefers the following move and thinks it is about 2% better than yours:
$$
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . X . . . . . X . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . B . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . . . , . . . . . O X . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
- Click Here To Show Diagram Code
[go]$$
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . . X . . . . . X . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . B . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . . . , . . . . . O X . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
Ian Butler wrote:2) Move 29: is it alive?
Yes, in fact, Lizzie thinks your first major mistake was responding to S8. For black 29, Lizzie thinks attaching to the bottom of the 4-4 stone at D4 is 18% better than defending at T6. And before T4, Lizzie thinks black had a 52% chance of winning.
Ian Butler wrote:3) Move 32: how would you try to tip the game in black's favor? White is getting a lead in potential. For example: where'd you play on the left side?
This is what prompted me to look at your game with Lizzie in the first place. In my experience, if you find yourself in a situation where you see your opponent has an advantage and you aren't sure what to do -- you've probably already made your mistake. My instinct (and Lizzie agrees) is that you should have played A in this position rather than blocking with B (playing at the intersection of two moyos?). Lizzie's second choice is the attachment at C. So, the left side is still big.
$$
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . X . . b . . |
$$ | . . . X . . . . . X . . . . . X . W . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . a . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . O O . |
$$ | . . . . . . . . . . . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . O X . X |
$$ | . . . . . . . . . . . . X . . O X . . |
$$ | . . c O . . . . . , . . . . . O X . . |
$$ | . . . . . . O . . X . . X . . O X . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
- Click Here To Show Diagram Code
[go]$$
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . X . . b . . |
$$ | . . . X . . . . . X . . . . . X . W . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . a . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . O O . |
$$ | . . . . . . . . . . . . . . . . O X . |
$$ | . . . . . . . . . . . . . . . O X . X |
$$ | . . . . . . . . . . . . X . . O X . . |
$$ | . . c O . . . . . , . . . . . O X . . |
$$ | . . . . . . O . . X . . X . . O X . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
Ian Butler wrote:4) Move 54: are my variations somewhat correct and thus could've killed (at least part of) white's invasion?
Can't answer this one definitively, but killing looks to be overly ambitious. I never found a sequence where white did not manage to live or escape.
Also, just a heads up, but you had a chance to play the corner sequence from the 3-3 invasion of the large knight enclosure that jlt suggested (
viewtopic.php?p=238986#p238986) at 35:
$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . 6 . . . . . .
$$ | . 4 . . . . . . .
$$ | . 3 O O 1 . . . .
$$ | . 5 X X O 2 O . .
$$ | . . . 7 X O . . .
$$ | . . . . . . . . .
$$ +------------------
- Click Here To Show Diagram Code
[go]$$B
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . 6 . . . . . .
$$ | . 4 . . . . . . .
$$ | . 3 O O 1 . . . .
$$ | . 5 X X O 2 O . .
$$ | . . . 7 X O . . .
$$ | . . . . . . . . .
$$ +------------------[/go]
This is a very good sequence to learn because usually white needs to play another local move to limit the impact of the aji of

. So, you get the invasion and get to retain sente.