OK, that's a question you could write a book on...
Reg 1) I think there is no blanket statement that fits here. Depends on the geography, the industry, the client, the project and even the people involved.
- Is a project of strategic importance for the consultancy?
- Does the client have the potential for long-term projects or is this a one-off?
- Are partners incentivized on revenue or on margins?
And a million more questions like these factor into that...
But in general, you are right in assuming that consultancies try to maintain some level of pricing, mostly to not set dangerous precedents.
Reg 2) No, it is not all about the rates. It's about the people and the true experience a company has (not what they write on their website). This may be less true for projects that occupy busloads of consultants at a time, but in strategy consulting, I have personally been on large projects (seven figures) where the clients (we're talking board members of Fortune 500 companies) made the project approval contingent on specific, individual people (project managers, not partners, btw) being on the project team. And not due to nepotism or corruption, but because they did not buy the brand, they wanted to buy these specific people. Basically at any (somewhat reasonable) price.
I have also seen projects where the CEO of one of the largest German (in that case) companies personally called the named project references to vet the consultancy's experience. And in that specific case, one of the MBBs (not saying which one) didn't stack up and where eliminated from the pitch.
reg 3) No clue.