Re: The reduction.
There's a 'rule' that says that when you are contacted by a stone you must gain liberties for that stone until it's stable. The diagonal white shoulder hit is a contact play. Any attachment to white's stone would also be a contact play. Anyway, white extends to gain liberties, and to build a wall that he hopes will provide profit (by attacking your corner maybe?). You must then extend to gain liberties yourself (also needs to remove a white liberty or be diagonal to a white stone). You can't hane or jump yet because locally white is much stronger.
After extending once white and black both have 5 liberties. Which is the minimum number of liberties that are stable. White
could take sente and move somewhere instead of gaining liberties. But he decides to push from behind once more so you don't have sente contact moves against his wall. When he extends, he reduces your liberties to 4. You
must extend once more to gain liberties to at least 5 (ideally no more than 6). When you jumped instead, that was a mistake.
White won't keep pushing you from behind. Why? Because if he does, it's gote. You don't need to respond in contact. You can jump and make shape, or play in another part of the board or whatever (actually, you should jump or build a base on the side, depending on if you want to live or run). If he wants to keep running he'll make a knight's move himself. But then he has to fall back a bit and you get some breathing room to do whatever.
...
When white wedged into the cut that was white going 'OMG roxxor Black fubar, I cut now'. If you've ever watched Day 9 Starcraft 2 videos, when a player goes for a crazy all-in attack after an opponent makes a mistake, he calls that 'getting a boner'. IMO white got a boner when he saw you screw up and wanted to capitalize on it immediately. (It maybe actually be the best refutation, but it seems pretty all-in to me).
Anyway, once you know that rule, it makes a lot of play like this make
way more sense. Pros almost always follow this rule, as do joseki. (
Contact Fights talks about this in great depth (I don't mean to keep spamming Wilcox's stuff, but it does a pretty good job of explaining this stuff and it seems to come up a lot)). The exceptions involve high level reading that always gets me in to trouble.
Afterwords, after extending, white should get sente (starting contact is usually gote) and will try to attack you by enclosing you inside his moyo or at least escaping with his stones (the reason A&D says white will slide). You try to build a base and live locally -or- run away to friendly stones and counter attack white. Reductions usually try to run.
I won't comment on anything else in the game to avoid making a fool of myself

But about this specific reduction, in total isolation on the board, I feel pretty confident I know what I'm talking about.