Sorry, I should have picked up on that: the rules regarding Heat & Experience were changed at a quite a late stage, after Tommy had designed the playbooks, and I completely missed that the old rule was still there.

To clarify: when you take heat, you mark experience and when experience alone reaches 5, reset it to zero and take an advance, just as with AW itself.

It's meant for one roll per interaction, whether that's a single NPC or a group and it isn't necessarily just when you ask them for a favour, but for when your actions impact them directly, i.e. you invite someone into your family home that they don't want there. Deal with it situationally, so one roll whether its a single NPC you're making trouble for a or a group of them; on a 10+, they turn their back on you until the situation changes, which is part of the conversation between the PCs and MC.

This should have also been listed under the moves the MC can make: it's largely intended as a hard move they can make against you after a miss in applicable situations, e.g. you've tried to argue the toss with them and they've turned your offer down flat, so now you check to see if they're prepared to deal with you at all.

No, when you lie low, you establish in the fiction how you are doing so, so you need to clearly state whose help you are getting and how; having heat won't effect this and won't require you to make trouble before you can try to lie low, but if you miss on the lie low move, then the MC might ask you to roll to see if this refusal makes trouble for you.

I hope that's been of help. :-)

[. . .]it's so important that the Battlebabe choose their connections, their friendships, their allegiances.

I'm currently studying Economics and Anthropology, and this thread got me thinking about how various real life unit of social organization map into Apocalypse World.