Fit the order of what you ask and when to who you are talking to.
In my line of work, for example, it's not unusual for the interview process to be:
Establish contact w. a recruiter (let's say it's external to the
company). Provide resume and agree to have it shared w. the company.
Answer basic questions to help recruiter sell you.
Contact is made with the first line of
recruitment internal to the company. Pass that communication
Go through some number of interviews (phone, video, in person) with some number of stakeholders within the company. Usually this includes the person to whom you will reporting and a sampling of the people you may be working with. Other types of analysis may be used (coding exercise, testing, presentations, etc)
Get a debrief from some variety of recruitment. Debrief ends in offer
The goal I have with make or break questions is to aim to get answers that are both accurate and time saving for everyone involved (but especially me!). It does me no good if the answers are not accurate, so I focus on that as a priority.
Here's how I'd break the questions down by phase in the above process:
1 - Outside recruiter - first contact
They can't be a great representative of the company. Don't expect accurate answers about work at home and child care - for example.
They do however, have the ability to verify:
contract vs. non-contract - this has to be explicitly clear to them before they start recruiting.
ball park of salary - it's true that I would not start at the negotiation but I've been called for positions that are 10,000s less that I would even consider. I usually give a ball park ("I'm looking in the mid 100K range") nothing too specific, but I really don't want the conversation to go past this phone call if we're on two different pages.
size and riskiness of company
location and existence of relocation package
must start by XYZ date. You can't easily get agreement on the latest you could possibly start yet (and who knows how long the process will take?), but you can be clear and say "I'm looking to start by XYZ date - any job that can do this will be my first pick".
They tend not to have much maneuverability. There's always the option of going forward with something that sounds like a no go, but which you may negotiate into something good. But that's at the risk of wasting your time.
2 - Recruitment w/in the company.
It never hurts to verify that the external recruiter is not sleazy. Besides, it makes you sound like researched and you care when you run through the description of the position that you have so far. Go through all the elements of set 1 that mattered to you.
It's also a good time to check on the Y/N of benefits - time off, health care, child care on campus -- all the stuff you may be able to read in a brochure from the HR department. Try not to scrutinize - try to hit the stuff that is make or break.
For the most part, the company will not create special benefit packages for YOU. It's been done in the right time and place, but I would not expect it to be the norm, so this a good time get info on the non-negotiable stuff.
3 - Talking with your actual boss.
This is the time when it's good to interview your boss. There's a huge bunch of make or break stuff that relates to the boss/employee relationship.
Keep in mind, however that you can't really get to a negotiation that is in your favor until your potential boss has gotten the feedback of his fellow stakeholders. He's probably not going to negotiate while he's in evaluation mode.
After 3, during or after 4 - the Offer.
Now is when you actually have some ability to influence outcomes. Maybe work at home options are unusual, but now that they've met you, they are willing to consider a trial. Maybe you will get a higher or lower salary package based on the value they think you will deliver.
It is the very end of the process, however.
On the job
There are a few cases where you may wish to wait, even on make or break conditions until your first day. One such thing is non-visible disabilities. Prejudice against groups of people with disabilities has lead many to get the job first, and ask for accommodations later.