1. How are the experience rules working out so far? I mean both "Good and Bad Experiences" as well as "advancement". How are they affecting play, and which parts do you find you use the most?
That's... quite a big question, and I'm not sure I know the answer. I think we're thinking of Bad Experiences as a more colorful version of hit points, but we haven't ever gotten to the point where a PC had marked 5 different BEs once - I'm sure we'll learn more about those over time.
"Good" experience plays a role in shaping player expectations, I believe. Browsing the list tells them what kind of people their characters are expected to be or become, whether that sets a bar to strive for, a foil to strive against, or a legitimation of planned courses of action ("Fuck this gang war shit! I need to take a break, and you know what, that's my chance to mark this "leave the city at my liberty" experience!").
Examining treasure is a lot of fun and it drives the game a lot, whether it leads to "advancement" in the strictest sense (PCs acquiring new skills and belongings) or just to a bout of high living. I look forward to the most complex choices being made, as they enrich the game immensely - such as when Iago recently started a publishing house specializing in pornography and satire in his spacious, half-crumbling house.
How do you decide how much and how often to put treasure in the characters' path?
I don't, really. Whenever the fictional situation justifies giving them valuable loot, a reward, payment or a bribe, I do so, and it's 1 unexamined treasure to each character involved, barring exceptional circumstances. This usually translates to 1-2 pieces of treasure per PC per session, but sometimes they get none at all.
2. Tell me more about "checking your equipment". It's an option in the Prepare move which has me a little puzzled. Do you create some tension, as MC, to make this particularly useful?
With the groups I play with, it's usually not on the table for the MC to make various substitutions or "surprises" based on the PCs' equipment. ("Oh, actually you can't find your knife today..." or "turns out that potions broke an hour ago, and is now spilled everywhere"). Generally, in the D&D tradition, characters' belongings are considered the player's prerogative, and are managed by the player. I like the idea in principle, however; it's got me thinking.
Do you think you do something like this, to make that option attractive to the players? Or has it fallen naturally out of an action sequence (e.g. "Hey, you tumbled down that railing just now. Want to check if anything broke...")?
Your "tumbled down a railing" example is the closest to what we're doing. Even so, it's the least frequently used of all the available RR&P options - but I think that's fine the way it is. It's for those times when it's not altogether certain whether the PCs have all of their weapons, armor and other equipment with them. For example, when Vetin realized she was wanted for questioning, she decided not to go back to her inn, where guards were waiting for her - but it wasn't altogether clear whether she was wearing her armor and carrying her spell tablet, or those things were left in her room.
The use of a Patient save to see whether they can wait long enough for a good moment is also an interesting game moment. Was it more like, "Let's see if you can bring yourself to do it!", or more like, "Let's see if you manage to do it without repercussions..."?
Those uses of the saving throw were very similar to Acting under (metaphorical) fire. In those circumstances, the objective was to leave the corpse somewhere visible, to send the Half Bat gang a clear "message", but not to be seen with the corpse and later recognized. I asked them for both Bold saves - to bring themselves to do it and do it with a straight face - and Patient saves to wait for and spot the perfect moment to act... in that case, the perfect moment to leave. The failed Patient save meant they had attracted unwanted attention. With saves, I always state this out loud when asking for one, like: "pass a difficult Patient save not to attract unwanted attention".