The most difficult part, and I think the last of the chunks on this topic: when do you do the asking?
Let me be clear: I don't think there are absolutes here. When you ask for the things you want is going to depend on the nature of your non-negotiables, what you want to ask for, and a lot of other things.
I think non-negotiables, if they seem applicable to the project in question, should be raised during the process of making the audition appointment. It might lead to you not even making the audition appointment. If you're a woman who has no nudity ever ever ever as a non-negotiable, and you see an audition notice which says that the character will be topless, you wouldn't go to that audition. A different woman might have a non negotiable of no nudity that is exploitative or gratuitous, and would inquire about the audition appointment, but ask to see a script or have a phone conversation with the director about what happens in the topless scene in order to make a decision about the nature of the nudity in the project. Super bad form: doing the audition, getting cast, and then saying "oh, by the way, I never take my clothes off for acting work" If it was a non-negotiable, this person has just wasted everyone's time. The production made it clear that going topless was a requirement for the role.
Now, if you're talking about the perks, the things that it would be nice to have, but that aren't requirements for you, these are things to ask about when the part is offered. And, outside of the tight casting timeline that often takes place in film/tv/commercials, it is perfectly fine when offered a role to say "thank you so much! I'd like to call you back in 4, 8 or even 24 hours to talk more about the project." Acknowledging that you've received their offer, you're excited by it, but then waiting to talk business until the initial adrenaline of getting the offer has worked it's way through your system. And then put on your business hat, and ask "is there any wiggle room in your stipend?" or "one of my goals this year is to increase my name recognition in this region - I'm hoping you'll have me be in the press photos for this project" They may say no, but they just might say yes. And, if they don't say yes (or aren't able to say yes) this time, you've built a framework for discussion on future projects.
Hoping this series of thoughts has been helpful. Let me know about how your negotiations go!